% -*-BibTeX-*-
%%% Alternative Cyrillic definitions are supplied in the event that
%%% cyracc.def is not loaded.
@Preamble{"\ifx \cedla \undefined \let \cedla = \c \fi" # "\ifx \cyr
\undefined \let \cyr = \relax \fi" # "\ifx \cprime
\undefined \def \cprime {$\mathsurround=0pt '$}\fi" #
"\ifx \prime \undefined \def \prime {'} \fi"}
%-----------------------------------------------------------------------
% Journal abbreviations:
@String{j-ACTA-METALL = "Acta Metallurgica"}
@String{j-ACTA-METALL-MATER = "Acta Metallurgica et Materialia"}
@String{j-ADV-PHYS = "Advances in Physics"}
@String{j-ANN-APPL-PROBAB = "Annals of Applied Probability"}
@String{j-ANN-INST-HENRI-POINCARE-B = "Annales de l'Institut Henri
Poincar{\'e}. Section B, Probabilit{\'e}s et
Statistiques"}
@String{j-ANN-MAT-PURA-APPL-4 = "Annali di Matematica Pura ed Applicata.
Series 4"}
@String{j-ANN-MATH-2 = "Annals of Mathematics (2)"}
@String{j-ANN-PHYS = "Annals of Physics"}
@String{j-ANN-PHYS-1900 = "Annalen der Physik (1900)"}
@String{j-ANN-REV-MATERIAL-SCI = "Annual Review of Materials Science"}
@String{j-ANN-SC-NORM-SUPER-PISA-CL-SCI = "Annali della Scuola Normale
Superiore di Pisa, Classe di Scienze"}
@String{j-APPL-MATH = "Applications of Mathematics"}
@String{j-APPL-MATH-MECH-ENGL-ED = "Applied Mathematics and Mechanics"}
@String{j-APPL-MATH-OPTIM = "Applied Mathematics and Optimization"}
@String{j-APPL-MECH-REV = "Applied Mechanics Reviews"}
@String{j-APPL-PHYS = "Applied Physics"}
@String{j-APPL-PHYS-LET = "Applied Physics Letters"}
@String{j-APPLIC-ANAL = "Applicable Analysis"}
@String{j-ARCH-MECH = "Archives of Mechanics = Archiwum Mechaniki
Stosowanej"}
@String{j-ARCH-RAT-MECH-ANAL = "Archive for Rational Mechanics and
Analysis"}
@String{j-ASYMPTOT-ANAL = "Asymptotic Analysis"}
@String{j-AUTOMATIC-REMOTE-CTL = "Automatic and Remote Control"}
@String{j-BOLL-UNIONE-MAT-ITAL = "Bollettino della Unione Matematica
Italiana"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-C-R-ACAD-SCI-PARIS = "Comptes Rendus de l'Acad{\'e}mie des
Sciences, Paris"}
@String{j-C-R-ACAD-SCI-PARIS-SER-AB = "Comptes Rendus Hebdomadaires des
S{\'e}ances de l'Acad{\'e}mie des Sciences.
S{\'e}ries A et B"}
@String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}rie I.
Math{\'e}matique"}
@String{j-CALC-VAR-PARTIAL-DIFFER-EQU = "Calculus of Variations and Partial
Differential Equations"}
@String{j-CALCOLO = "Calcolo"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics"}
@String{j-COMM-PARTIAL-DIFF-EQNS = "Communications in Partial Differential
Equations"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMMUN-MATH-PHYS = "Communications in Mathematical Physics"}
@String{j-COMP-MECH = "Computational Mechanics"}
@String{j-COMP-STRUCTURES = "Computers and Structures"}
@String{j-COMPUT-MECH = "Computational Mechanics"}
@String{j-COMPUT-METH-APPL-MECH-ENG = "Computer Methods in Applied Mechanics
and Engineering"}
@String{j-CONTIN-MECH-THERMODYN = "Continuum Mechanics and Thermodynamics"}
@String{j-CONTROL-CYBERN = "Control and Cybernetics"}
@String{j-DELFT-PROG-REP = "Delft Progress Report"}
@String{j-DIFFER-URAVN-MINSK-1965 = "Differencial'nye Uravnenija (Minsk,
1965)"}
@String{j-DIN-SPLOS-SREDY = "Dinamika Sploshnoi Sredy"}
@String{j-DOC-MATH = "Documenta Mathematica"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii Nauk SSSR"}
@String{j-DUKE-MATH = "Duke Mathematical Journal"}
@String{j-ENG-TRANS = "Engineering Transactions"}
@String{j-EUR-J-APPL-MATH = "European Journal of Applied Mathematics"}
@String{j-EUR-J-MECH-A-SOLIDS = "European Journal of Mechanics, A, Solids."}
@String{j-EW-J-NUM-MATH = "East-West Journal of Numerical Mathematics"}
@String{j-IMA-J-APPL-MATH = "IMA Journal of Applied Mathematics"}
@String{j-IMP-COMP-SCI-ENG = "Impact of Computing in Science and
Engineering"}
@String{j-INT-J-DAMAGE-MECH = "International Journal of Damage Mechanics"}
@String{j-INT-J-ENG-SCI = "International Journal of Engineering
Science"}
@String{j-INT-J-HEAT-MASS-TRANSFER = "International Journal of Heat and Mass
Transfer"}
@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical
Methods in Engineering"}
@String{j-INT-J-SOLIDS-STRUCT = "International Journal of Solids and
Structures"}
@String{j-INT-SER-NUMER-MATH = "International Series of Numerical
Mathematics = Internationale Schriftenreihe
zur Numerischen Mathematik = S{\'e}rie
Internationale d'Analyse Num{\'e}rique"}
@String{j-INVERSE-PROBLEMS = "Inverse Problems"}
@String{j-ISRAEL-J-MATH = "Israel Journal of Mathematics"}
@String{j-IZV-AKAD-ARM-SSR-MEH = "Izvestiia Akademii Nauk Armianskoi SSR.
Mekhanika = Haykakan SSR Gitut'yunneri
Akademiayi Teghekagir. Mekhanika"}
@String{j-IZV-AKAD-NAUK-SSSR-MAT = "Izvestiia Akademii Nauk. USSR Seriia
Matematicheskaia (Moscow)"}
@String{j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA = "Izvestiia Akademii Nauk SSSR.
Mekhanika Tverdogo Tela"}
@String{j-IZV-ROSS-AKAD-NAUK-SER-MAT = "Izvestiia Rossiiskoi Akademii Nauk.
Seriia Matematicheskaia"}
@String{j-IZV-VYSS-UCEBN-ZAVED-MAT = "Izvestiia Vysshikh Uchebnykh Zavedenii.
Matematika"}
@String{j-J-APPL-MATH-MECH = "Journal of Applied Mathematics and
Mechanics"}
@String{j-J-APPL-MECH = "Journal of Applied Mechanics"}
@String{j-J-APPL-PHYS = "Journal of Applied Physics"}
@String{j-J-CHEM-PHYS = "Journal of Chemical Physics"}
@String{j-J-CONVEX-ANAL = "Journal of Convex Analysis"}
@String{j-J-DIFFER-EQU = "Journal of Differential Equations"}
@String{j-J-DYN-CONTROL-SYST = "Journal of Dynamical and Control Systems"}
@String{j-J-ELAST = "Journal of Elasticity"}
@String{j-J-ENG-MATER-TECHNOL = "Journal of Engineering Materials and
Technology"}
@String{j-J-ENG-MECH = "Journal of Engineering Mechanics"}
@String{j-J-EXP-THEOR-PHYS = "Journal of Experimental and Theoretical
Physics (JETP)"}
@String{j-J-FLUID-MECH = "Journal of Fluid Mechanics"}
@String{j-J-FUNCT-ANAL = "Journal of Functional Analysis"}
@String{j-J-GEOM-ANAL = "Journal of Geometric Analysis"}
@String{j-J-GEOPHYS-RES = "Journal of Geophysical Research"}
@String{j-J-GLOBAL-OPT = "Journal of Global Optimization"}
@String{j-J-MATER-SCI-LETT = "Journal of Materials Science Letters"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-MATH-MECH = "Journal of Mathematics and Mechanics"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MATH-PURES-APPL = "Journal de Math{\'e}matiques Pures et
Appliqu{\'e}es"}
@String{j-J-MEC = "Journal de M{\'e}canique"}
@String{j-J-MECH-PHYS-SOLIDS = "Journal of the Mechanics and Physics of
Solids"}
@String{j-J-OPT-THEORY-APPL = "Journal of Optimization Theory and
Applications"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and
General)"}
@String{j-J-PHYS-C = "Journal of Physics C: Solid State Physics"}
@String{j-J-PHYS-D = "Journal of Physics D: Applied Physics"}
@String{j-J-R-AERONAUT-SOC = "Journal of the Royal Aeronautical Society"}
@String{j-J-STAT-PHYS = "Journal of Statistical Physics"}
@String{j-J-STRUCT-MECH = "Journal of Structural Mechanics"}
@String{j-J-THERM-STRESS = "Journal of Thermal Stresses"}
@String{j-JAPAN-J-MATH-N-S = "Japanese Journal of Mathematics. New
Series"}
@String{j-LATV-MAT-EZEG = "Latviiskii Matematicheskii Ezhegodnik"}
@String{j-LECT-NOTES-PHYSICS = "Lecture Notes in Physics"}
@String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"}
@String{j-MANUSCR-MATH = "Manuscripta Mathematica"}
@String{j-MAT-SB = "Matematicheskii Sbornik"}
@String{j-MAT-SB-MOSK = "Matematicheskii Sbornik / Izdavaemyi
Moskovskim Matematicheskim Obshchestvom =
Recueil Math{\'e}matique de la
Soci{\'e}t{\'e} Math{\'e}matique de Moscou"}
@String{j-MAT-ZAMETKI = "Matematicheskie Zametki"}
@String{j-MATH-COMP-MODELLING = "Mathematical and Computer Modelling"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-MECH-SOLIDS = "Mathematics and Mechanics of Solids : MMS"}
@String{j-MATH-MODEL-NUM-ANA = "Mathematical Modelling and Numerical
Analysis = Modelisation Math{\'e}matique et
Analyse Num{\'e}rique: $M^2AN$"}
@String{j-MATH-MODELS-METHODS-APPL-SCI = "Mathematical Models and Methods in
Applied Sciences"}
@String{j-MATH-NACHR = "Mathematische Nachrichten"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MECCANICA-MILAN = "Meccanica (Milan)"}
@String{j-MECH-MATER = "Mechanics of Materials: An International
Journal"}
@String{j-MECH-RESEARCH-COMM = "Mechanics Research Communications"}
@String{j-MECH-SOLIDS = "Mechanics of Solids"}
@String{j-MECHAN-STRUCT-MACH = "Mechanics of Structures and Machines"}
@String{j-METALL-TRANS-A-PHYS-METALL-MATER-SCI = "Metallurgical Transactions.
A, Physical Metallurgy and Materials
Science"}
@String{j-NAMS = "Notices of the American Mathematical
Society"}
@String{j-NATURE = "Nature"}
@String{j-NONLINEAR-ANAL = "Nonlinear Analysis, Theory, Methods and
Applications"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUMER-FUNCT-ANAL-OPTIM = "Numerical Functional Analysis and
Optimization"}
@String{j-OPT-CTL-APPL-METH = "Optimal Control Applications and Methods"}
@String{j-OPTIMIZATION = "Optimization"}
@String{j-OPTIMIZATSIIA = "Optimizatsiya"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PHIL-MAGAZINE = "Philosophical Magazine"}
@String{j-PHILOS-TRANS-R-SOC-LOND = "Philosophical Transactions of the Royal
Society of London"}
@String{j-PHILOS-TRANS-R-SOC-LOND-SER-A = "Philosophical Transactions of the
Royal Society of London Series A"}
@String{j-PHYS-FLUIDS = "Physics of Fluids"}
@String{j-PHYS-LET-A = "Physics Letters A"}
@String{j-PHYS-REP = "Physics Reports"}
@String{j-PHYS-REV = "Physical Review"}
@String{j-PHYS-REV-A = "Physical Review A (Atomic, Molecular, and
Optical Physics)"}
@String{j-PHYS-REV-B = "Physical Review B (Solid State)"}
@String{j-PHYS-REV-LET = "Physical Review Letters"}
@String{j-PHYS-STATUS-SOLIDI = "Physica Status Solidi"}
@String{j-PHYS-STATUS-SOLIDI-B-BASIC-RES = "Physica Status Solidi. B, Basic
Research"}
@String{j-PHYSICA = "Physica"}
@String{j-PHYSICA-D = "Physica. D, Nonlinear Phenomena"}
@String{j-POTENTIAL-ANAL = "Potential Analysis: An International
Journal Devoted to the Interactions between
Potential Theory, Probability Theory,
Geometry and Functional Analysis"}
@String{j-PRIKL-MAT-MEH = "Prikladnaia Matematika i Mekhanika (PMM)=
Applied Mathematics and Mechanics"}
@String{j-PRIKL-PROBLEMY-PROCH-I-PLAST = "Gor{\cprime}kovski\u\i\
Gosudarstvenny\u\i\ Universitet imeni N. I.
Lobachevskogo. Prikladnye Problemy
Prochnosti i Plastichnosti"}
@String{j-PROB-ENG-MECH = "Probabilistic Engineering Mechanics"}
@String{j-PROBAB-THEORY-RELAT-FIELDS = "Probability Theory and Related Fields"}
@String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical
Society"}
@String{j-PROC-LONDON-MATH-SOC = "Proceedings of the London Mathematical
Society. Third Series"}
@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
Sciences of the United States of America"}
@String{j-PROC-R-SOC-EDINB = "Proceedings of the Royal Society of
Edinburgh"}
@String{j-PROC-R-SOC-EDINB-SECT-A-MATH = "Proceedings of the Royal Society of
Edinburgh. Section A, Mathematical and
Physical Sciences"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
Society of London. Series A, Mathematical
and Physical Sciences"}
@String{j-PROC-STEKLOV-INST-MATH = "Trudy Matematicheskogo Instituta imeni V.
A. Steklova = Proceedings of the Steklov
Institute of Mathematics"}
@String{j-QUART-APPL-MATH = "Quarterly of Applied Mathematics"}
@String{j-QUART-J-MECH-APPLIED-MATH = "Quarterly Journal of Mechanics and
Applied Mathematics"}
@String{j-REND-MAT-APPL-1981 = "Rendiconti di Matematica e Delle Sue
Applicazioni (1981)"}
@String{j-REV-GEOPHYS-SPACE-PHYS = "Reviews of Geophysics and Space Physics"}
@String{j-RIC-MAT = "Ricerche di Matematica (Napoli)"}
@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}
@String{j-RUSS-J-MATH-PHYS = "Russian Journal of Mathematical Physics"}
@String{j-RUSS-J-NUM-ANAL-MATH-MODEL = "Russian Journal of Numerical Analysis
and Mathematical Modelling"}
@String{j-RUSS-MATH-SURV = "Russian Mathematical Surveys"}
@String{j-SCR-METALL = "Scripta Metallurgica"}
@String{j-SET-VALUED-ANAL = "Set-Valued Analysis"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-CONTROL = "SIAM Journal on Control"}
@String{j-SIAM-J-CONTROL-OPTIM = "SIAM Journal on Control and Optimization"}
@String{j-SIAM-J-MATH-ANA = "SIAM Journal on Mathematical Analysis"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-OPT = "SIAM Journal on Optimization"}
@String{j-SIB-MAT-Z = "Sibirskii Matematicheskii Zhurnal"}
@String{j-SIBERIAN-ADV-MATH = "Siberian Advances in Mathematics"}
@String{j-SOLID-STATE-PHYS-N-Y-1955 = "Solid State Physics (New York. 1955)"}
@String{j-SOV-PHYS-JETP = "Soviet Physics, JETP"}
@String{j-SOV-PHYS-SOLID-STATE = "Soviet Physics, Solid State"}
@String{j-SOVIET-MATH-DOKL = "Soviet Mathematics. Doklady"}
@String{j-SOVIET-PHYS-DOKL = "Soviet Physics---Doklady"}
@String{j-STRUCT-OPTIM = "Structural Optimization"}
@String{j-UKR-MAT-Z = "Ukrainskii Matematicheskii Zhurnal"}
@String{j-USP-MEH = "Uspekhi Mekhaniki = Advances in Mechanics"}
@String{j-WASSERWIRTSCHAFT = "Wasserwirtschaft"}
@String{j-WAVE-MOTION = "Wave Motion"}
@String{j-Z-ANAL-ANWEND = "Zeitschrift f{\"u}r Analysis und ihre
Anwendungen"}
@String{j-Z-ANGE-MATH-MECH = "Zeitschrift f{\"u}r Angewandte Mathematik
und Mechanik"}
@String{j-Z-EKSP-TEOR-FIZ = "Zhurnal Eksperimental'noi i Teoreticheskoi
Fiziki / Akademiia Nauk SSSR"}
@String{j-Z-TEH-FIZ = "Zhurnal Tehniceskoj Fiziki"}
@String{j-Z-VYCISL-MAT-MAT-FIZ = "Zhurnal Vychislitel'noi Matematiki i
Matematicheskoi Fiziki"}
@String{j-ZAP-NAUC-SEMIN-LENINGR-OTD-ORDENA = "Zapiski Nauchnogo Seminara LOMI"}
%-----------------------------------------------------------------------
% Publisher abbreviations:
@String{pub-A-K-PETERS = "A. K. Peters, Ltd."}
@String{pub-A-K-PETERS:adr = "Wellesley, MA"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI"}
@String{pub-AP = "Academic Press"}
@String{pub-AP:adr = "New York"}
@String{pub-BIRKHAUSER = "Birkh{\"a}user Verlag"}
@String{pub-BIRKHAUSER-BOSTON = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA"}
@String{pub-BIRKHAUSER:adr = "Basel, Switzerland"}
@String{pub-CHAPMAN-HALL = "Chapman and Hall, Ltd."}
@String{pub-CHAPMAN-HALL:adr = "London"}
@String{pub-CLARENDON-PRESS = "Clarendon Press"}
@String{pub-CLARENDON-PRESS:adr = "Oxford, UK"}
@String{pub-CRC = "CRC Press"}
@String{pub-CRC:adr = "2000 N.W. Corporate Blvd., Boca Raton, FL
33431-9868"}
@String{pub-CUP = "Cambridge University Press"}
@String{pub-CUP:adr = "Cambridge, UK"}
@String{pub-DOVER = "Dover Publications, Inc."}
@String{pub-DOVER:adr = "New York"}
@String{pub-DUNOD = "Dunod"}
@String{pub-DUNOD:adr = "Paris, France"}
@String{pub-EH = "Ellis Horwood Ltd."}
@String{pub-EH:adr = "New York"}
@String{pub-ELS = "Elsevier"}
@String{pub-ELS:adr = "Amsterdam, The Netherlands"}
@String{pub-EYROLLES = "Eyrolles"}
@String{pub-EYROLLES:adr = "Paris, France"}
@String{pub-GRUYTER = "Walter de Gruyter"}
@String{pub-GRUYTER:adr = "New York, USA and Berlin, Germany"}
@String{pub-INTERSCI = "Interscience Publishers"}
@String{pub-INTERSCI:adr = "New York"}
@String{pub-KLUWER = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr = "Dordrecht. Boston. London"}
@String{pub-LONGMAN = "Longman Scientific and Technical"}
@String{pub-LONGMAN:adr = "Harlow, Essex, UK"}
@String{pub-MACMILLAN = "MacMillan Publishing Company"}
@String{pub-MACMILLAN:adr = "New York"}
@String{pub-MASSON = "Masson Editeur"}
@String{pub-MASSON:adr = "Masson, France"}
@String{pub-MCGRAW-HILL = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr = "New York"}
@String{pub-MIR = "Mir Publishers"}
@String{pub-MIR:adr = "Moscow, Russia"}
@String{pub-NAUKA = "Nauka"}
@String{pub-NAUKA:adr = "Moscow, Russia"}
@String{pub-NH = "North-Holland Publishing Co."}
@String{pub-NH:adr = "Amsterdam, The Netherlands"}
@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PERGAMON = "Pergamon"}
@String{pub-PERGAMON:adr = "New York"}
@String{pub-PH = "Pren{\-}tice-Hall"}
@String{pub-PH:adr = "Upper Saddle River, NJ 07458"}
@String{pub-PITMAN = "Pitman Publishing Ltd."}
@String{pub-PITMAN:adr = "London"}
@String{pub-PLENUM = "Plenum Press"}
@String{pub-PLENUM:adr = "New York; London"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ"}
@String{pub-SIAM = "SIAM Press"}
@String{pub-SIAM:adr = "Philadelphia, PA"}
@String{pub-SPIE = "SPIE Optical Engineering Press"}
@String{pub-SPIE:adr = "Bellingham, WA"}
@String{pub-SV = "Springer-Verlag"}
@String{pub-SV:adr = "Berlin; Heidelberg; London; etc."}
@String{pub-TEUBNER = "Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart; Leipzig"}
@String{pub-U-CHICAGO = "University of Chicago Press"}
@String{pub-U-CHICAGO:adr = "Chicago, IL"}
@String{pub-WCP = "Wellesley-Cambridge Press"}
@String{pub-WCP:adr = "Wellesley, MA"}
@String{pub-WI = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WI:adr = "New York"}
@String{pub-WILEY = "John Wiley and Sons"}
@String{pub-WILEY:adr = "New York; London; Sydney"}
@String{pub-WORLD-SCI = "World Scientific Publishing Co."}
@String{pub-WORLD-SCI:adr = "Singapore; Philadelphia; River Edge, NJ"}
%-----------------------------------------------------------------------
% Bibliography entries, sorted by citation label:
@Book{Abramowitz:1965:HMF,
author = "M. Abramowitz and I. A. Stegun",
title = "Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xiv + 1046",
year = "1965",
LCCN = "QA47.A161 1972; QA 55 A16h 1972",
}
@Article{Achtziger:1992:EDB,
author = "W. Achtziger and M. P. Bend\-s{\o}e and A. {Ben-Tal}
and J. Zowe",
title = "Equivalent displacement based formulations for maximum
strength truss topology design",
journal = j-IMP-COMP-SCI-ENG,
volume = "4",
number = "4",
pages = "315--345",
year = "1992",
CODEN = "ICOEEK",
ISSN = "0899-8248",
fjournal = "Impact of Computing in Science and Engineering",
}
@Article{Achtziger:1998:BEP,
author = "W. Achtziger and M. P. Bend\-s{\o}e and J. E. Taylor",
title = "Bounds on the effect of progressive structural
degradation",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "46",
number = "6",
pages = "1055--1087",
year = "1998",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Book{Akhiezer:1962:CV,
author = "N. Akhiezer",
title = "The calculus of variations",
publisher = "Blaisdell Publishing Co. (A Division of Random House,
Inc.)",
address = "New York; London",
pages = "viii + 248",
year = "1962",
note = "Translated from the Russian by Aline H. Frink. A
Blaisdell Book in the Pure and Applied Sciences.",
}
@Article{Allaire:1993:EOB,
author = "G. Allaire and R. V. Kohn",
title = "Explicit optimal bounds on the elastic energy of a
two-phase composite in two space dimensions",
journal = j-QUART-APPL-MATH,
volume = "LI",
number = "4",
pages = "675--699",
month = dec,
year = "1993",
CODEN = "QAMAAY",
ISSN = "0033-569X",
}
@Article{Allaire:1993:HNP,
author = "G. Allaire and F. Murat",
title = "Homogenization of the {Neumann} problem with
nonisolated holes",
journal = j-ASYMPTOT-ANAL,
volume = "7",
number = "2",
pages = "81--95",
year = "1993",
CODEN = "ASANEZ",
ISSN = "0921-7134",
note = "With an appendix written jointly with A. K.
Nandakumar.",
fjournal = "Asymptotic Analysis",
}
@Article{Allaire:1993:OBE,
author = "G. Allaire and R. V. Kohn",
title = "Optimal bounds on the effective behavior of a mixture
of two well-ordered elastic materials",
journal = j-QUART-APPL-MATH,
volume = "LI",
number = "4",
pages = "643--674",
month = dec,
year = "1993",
CODEN = "QAMAAY",
ISSN = "0033-569X",
}
@Article{Allaire:1993:ODM,
author = "G. Allaire and R. V. Kohn",
title = "Optimal design for minimum weight and compliance in
plane stress using extremal microstructures",
journal = j-EUR-J-MECH-A-SOLIDS,
volume = "12",
number = "6",
pages = "839--878",
year = "1993",
CODEN = "EJASEV",
ISSN = "0997-7538",
}
@TechReport{Allaire:1993:TSC,
author = "G. Allaire and A. Braides and G. Buttazzo and A.
Defranceschi and L. V. Gibiansky",
title = "Two-Scale Convergence and Homogenization of Periodic
Structures",
number = "Ref. 140/93/M",
institution = "SISSA ISAS",
year = "1993",
abstract = "Asymptotic analysis of periodic structures; two-scale
convergence; homogenization of a second order elliptic
equation; application to fluid flow in porous media;
estimate of the pressure in a porous medium",
}
@TechReport{Allaire:1994:MSC,
author = "G. Allaire and M. Briane",
title = "Multi-scale convergence and reiterated
homogenization",
institution = "Publications du Laboratoire d'Analyse Num{\'e}rique",
year = "1994",
abstract = "This paper generalizes the notion of two-scale
convergence to the case of multiple se\-parat\-ed
scales of periodic oscillations. It allows to introduce
a multi-scale convergence method for the reiterated
homogenization of partial differential equations with
oscillating coefficients. This new method is applied to
a model problem with a finite or infinite numer of
microscopic scales, namely the homogenization of the
heat equation in a composite material. Finally, it is
generalized to handle the homogenization of the
{Neumann} problem in a perforated domain.",
}
@Article{Allaire:1994:OLB,
author = "G. Allaire and R. V. Kohn",
title = "Optimal lower bounds on the elastic energy of a
composite made from two non well-ordered isotropic
materials",
journal = j-QUART-APPL-MATH,
volume = "LII",
number = "2",
pages = "311--333",
year = "1994",
CODEN = "QAMAAY",
ISSN = "0033-569X",
}
@Article{Allaire:1997:SOH,
author = "G. Allaire and E. Bonnetier and G. A. Francfort and F.
Jouve",
title = "Shape optimization by the homogenization method",
journal = j-NUM-MATH,
volume = "76",
number = "1",
pages = "27--68",
year = "1997",
CODEN = "NUMMA7",
ISSN = "0029-599X",
fjournal = "Numerische Mathematik",
}
@Article{Allaire:19xx:BWH,
author = "G. Allaire and C. Conca",
fullauthor = "G. Allaire and Carlos Conca",
title = "{Bloch} Wave Homogenization for a Spectral Problem in
Fluid-Solid Structures",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "??",
number = "??",
pages = "??--??",
month = "??",
year = "19xx",
CODEN = "AVRMAW",
ISSN = "0003-9527",
note = "To appear.",
abstract = "This paper is concerned with the study of the
vibrations of a model of a coupled fluid-solid periodic
structure. As the period goes to zero, an asymptotic
analysis of the spectrum (i.e., the set of
eigenfrequencies) is performed. By introducing a new
method, the so-called Block wave homogenization method
(which is a blend of two-scale convergence and {Bloch}
wave decomposition), the limit spectrum is completely
characterized. It is made of a macroscopic or
homogenized part, and of a microscopic or {Bloch} wave
part. The main feature of the limit spectrum is that it
is purely essential, and mainly continuous.",
keywords = "homogenization, {Bloch} waves, spectral analysis,
fluid-solid structures",
}
@InCollection{Armand:1984:OCT,
author = "{J.-L}. Armand and K. A. Lurie and A. V. Cherkaev",
editor = "E. Atrek and R. H. Gallagher and K. M. Ragsdell and O.
C. Zienkeiwicz",
booktitle = "New Directions in optimal structural design",
title = "Optimal control theory and structural design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "211--229",
year = "1984",
}
@InCollection{Arora:1998:OSS,
author = "J. S. Arora",
editor = "C. T. Leondes",
booktitle = "Structural Dynamical Systems: Computational
Technologies and Optimization",
title = "Optimization of Structures subject to dynamical
loads",
publisher = "Gordon and Breach Science Publ.",
pages = "1--73",
year = "1998",
}
@Book{Arthurs:1980:CVP,
author = "A. M. Arthurs",
title = "Complementary variational principles",
publisher = pub-CLARENDON-PRESS,
address = pub-CLARENDON-PRESS:adr,
edition = "Second",
pages = "vii + 154 + (loose errata)",
year = "1980",
ISBN = "0-19-853532-5",
note = "Oxford Mathematical Monographs.",
}
@Article{Artola:1995:RUP,
author = "M. Artola and L. Tartar",
title = "Un r{\'e}sultat d'unicit{\'e} pour une classe de
probl{\`e}mes paraboliques quasi-lin{\'e}aires",
journal = j-RIC-MAT,
volume = "44",
number = "2",
pages = "409--420",
year = "1995",
CODEN = "RCMTAE",
ISSN = "0035-5038",
fjournal = "Ricerche di Matematica",
xxyear = "1996",
}
@Article{Asaro:1975:NUT,
author = "R. J. Asaro and D. M. Barnett",
title = "The non-uniform transformation strain problem for an
anisotropic ellipsoidal inclusion",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "23",
pages = "77--83",
year = "1975",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Ashby:1991:ONM,
author = "M. F. Ashby",
title = "Overview {No}. 92: {Materials} and shape",
journal = j-ACTA-METALL-MATER,
volume = "39",
number = "6",
pages = "1025--1039",
year = "1991",
CODEN = "AMATEB",
ISSN = "0956-7151",
}
@Article{Astala:1998:QMT,
author = "K. Astala and M. Miettinen",
title = "On quasiconformal mappings and $2$-dimensional
${G}$-closure problems",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "143",
number = "3",
pages = "207--240",
year = "1998",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Book{Atkin:1990:ITE,
author = "R. J. Atkin and N. Fox",
title = "An Introduction to the Theory of Elasticity",
publisher = "Longman",
address = "London",
year = "1990",
}
@Article{Auriault:1994:MMH,
author = "J.-L. Auriault and H. I. Ene",
title = "Macroscopic modelling of heat transfer in composites
with interfacial thermal barrier",
journal = j-INT-J-HEAT-MASS-TRANSFER,
volume = "37",
number = "18",
pages = "2885--2892",
year = "1994",
CODEN = "IJHMAK",
ISSN = "0017-9310",
abstract = "Macroscopic modelling of heat transfer in composites
in the presence of interfacial thermal resistance is
determined from a description at the heterogeneity
scale using a method of double-scaled asymptotic
developments. The analysis shows five different models.
Their domains of validity are defined by the value of a
dimensionless parameter. That permits the determination
of the correct model for a given macroscopic boundary
value problem. The models for a binary composite are
shown to belong to two main types: one-temperature and
two-temperature field models.",
}
@Article{Avellaneda:1987:IHD,
author = "M. Avellaneda",
title = "Iterated homogenization, differential effective medium
theory, and applications",
journal = j-COMM-PURE-APPL-MATH,
volume = "40",
pages = "803--847",
year = "1987",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
}
@Article{Avellaneda:1987:OBM,
author = "M. Avellaneda",
title = "Optimal Bounds and Microgeometries for Elastic
Two-Phase Composites",
journal = j-SIAM-J-APPL-MATH,
volume = "47",
number = "6",
pages = "1216--1228",
year = "1987",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
}
@Article{Avellaneda:1988:ECP,
author = "M. Avellaneda and A. V. Cherkaev and K. A. Lurie and
G. W. Milton",
title = "On the effective conductivity of polycrystals and a
three-dimensional phase interchange inequality",
journal = j-J-APPL-PHYS,
volume = "63",
pages = "4989--5003",
year = "1988",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@InProceedings{Avellaneda:1989:BEE,
author = "M. Avellaneda and G. W. Milton",
editor = "D. Hui and T. J. Kozik",
booktitle = "Composite {Material Technology}",
title = "Bounds on the Effective Elastic Tensor of Composites
based on Two-Point Correlations",
publisher = "ASME",
address = "",
pages = "89--93",
month = "",
year = "1989",
}
@Article{Avellaneda:1989:OBE,
author = "M. Avellaneda and G. W. Milton",
title = "Optimal bounds on the effective bulk modulus of
polycrystals",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "824--837",
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Avellaneda:1990:ECA,
author = "M. Avellaneda and O. Bruno",
title = "Effective conductivity and average polarizability of
random polycrystals",
journal = j-J-MATH-PHYS,
volume = "31",
number = "8",
pages = "2047--2056",
year = "1990",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
MRnumber = "MR91f:82070",
fjournal = "Journal of Mathematical Physics",
}
@Article{Avellaneda:1996:CCP,
author = "M. Avellaneda and A. V. Cherkaev and L. V. Gibiansky
and G. W. Milton and M. Rudelson",
title = "A complete characterization of the possible bulk and
shear moduli of planar polycrystals",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "44",
number = "7",
pages = "1179--1218",
month = "????",
year = "1996",
CODEN = "JMPSA8",
ISSN = "0022-5096",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
searchkey = "au:cherkaev, a",
}
@TechReport{B.e:1993:CPD,
author = "M. B.e and A. Damlamian and P. Donato",
title = "${H}$-convergence for perforated domains",
institution = "Publications du Laboratoire d'Analyse Num{\'e}rique,
Universit{\'e} Pierre et Marie Curie",
year = "1993",
abstract = "In this paper, the $H$-convergence of F. Murat and L.
Tartar is extended to the case of perforated materials.
This extension is denoted $H^0$-convergence. The main
properties of H-convergence are then shown to hold for
$H^0$-convergence, including the compactness theorem.
Also, P. Donato's estimate for the difference of two
H-limits is generalized to this case, in which the
measure of the symmetric difference of the two families
of holes appears. Finally, an $H^0$-convergence result
is obtained for a material perforated by a B.e
(non-periodic) lattice of spherical holes: an explicit
formula for the $H^0$-limit is given which generalizes
the result of D. Cioranescu and J. Saint Jean Paulin
for the periodic case.",
}
@Article{B.e:1993:TMN,
author = "M. B.e",
title = "Three Models of Non Periodic Fibrous Materials
Obtained by Homogenization",
journal = j-MATH-MODEL-NUM-ANA,
volume = "27",
number = "6",
pages = "759--775",
year = "1993",
CODEN = "RMMAEV",
ISSN = "0764-583X",
abstract = "We describe here three models of fibrous materials in
conduction (the results apply as well in elasticity).
The fibers are not periodically arranged but their
orientation varies continuously in the material. The
human heart is an example of such a material. The
models are obtained through the homogenization of the
fibrous structure.",
}
@Article{Backus:1962:LWE,
author = "G. E. Backus",
title = "Long-wave elastic anisotropy produced by horizontal
layering",
journal = j-J-GEOPHYS-RES,
volume = "67",
pages = "4427--4440",
year = "1962",
CODEN = "JGREA2",
ISSN = "0148-0227",
}
@Article{Backus:1970:LWE,
author = "G. E. Backus",
title = "A geometrical picture of anisotropic elastic tensors",
journal = j-REV-GEOPHYS-SPACE-PHYS,
volume = "8",
pages = "633--671",
year = "1970",
CODEN = "RGPSBL",
ISSN = "0034-6853",
}
@Article{Baker:1968:SRI,
author = "G. A. Baker",
title = "Some rigorous inequalities satisfied by the
ferromagnetic {Ising} model in a magnetic field",
journal = j-PHYS-REV-LET,
volume = "20",
pages = "990--992",
year = "1968",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Book{Bakhvalov:1989:HAP,
author = "N. S. Bakhvalov and G. P. Panasenko",
title = "Homogenization: Averaging Processes in Periodic
Media",
publisher = pub-KLUWER,
address = "Dordrecht/Boston/London",
year = "1989",
}
@Article{Bakhvalov:1990:NIA,
author = "N. S. Bakhvalov and A. Knyazev",
title = "A new iterative algorithm for solving problems of the
fictitious flow method for elliptic equations",
journal = j-SOVIET-MATH-DOKL,
volume = "41",
number = "3",
pages = "481--485",
year = "1990",
ISSN = "0197-6788",
}
@Article{Bakhvalov:1991:ECA,
author = "N. S. Bakhvalov and A. Knyazev",
title = "Efficient computation of averaged characteristics of
composites of a periodic structure of essentially
different materials",
journal = j-SOVIET-MATH-DOKL,
volume = "42",
number = "1",
pages = "57--62",
year = "1991",
ISSN = "0197-6788",
}
@InCollection{Bakhvalov:1991:MEC,
author = "N. S. Bakhvalov and A. Knyazev",
editor = "G. I. Marchuk",
booktitle = "Computational Processes and Systems, No. 8",
title = "Methods of effective computation of homogenized
properties for the composites with a periodic structure
which consist of essentially different components",
publisher = pub-NAUKA,
address = "Moscow",
pages = "52--94",
year = "1991",
note = "In Russian.",
comment = "Methods for the effective computation of averaged
characteristics of composites of periodic structure
consisting of essentially different materials",
}
@Article{Bakhvalov:1992:EIM,
author = "N. S. Bakhvalov and A. Knyazev",
title = "An efficient iterative method for solving the
{Lam{\'e}} equations for almost incompressible media
and {Stokes}' equations",
journal = j-SOVIET-MATH-DOKL,
volume = "44",
number = "1",
pages = "4--9",
year = "1992",
ISSN = "0197-6788",
}
@InProceedings{Bakhvalov:1994:FDM,
author = "N. S. Bakhvalov and A. Knyazev",
editor = "G. I. Marchuk",
booktitle = "Numerical Methods and Applications",
title = "Fictitious domain methods and computation of
homogenized properties of composites with a periodic
structure of essentially different components",
publisher = pub-CRC,
address = "Boca Raton",
pages = "221--276",
year = "1994",
abstract = "There are many important physical problems that can be
modeled using partial differential equations (PDE) with
discontinuous coefficients. Drops of the coefficients
may be very large. We consider one class of those
problems concerning composites of essentially different
components. Composites or composite materials are said
to be media with a large number of non homogeneous
inclusions with small sizes at least along one
direction. Stationary states of that media is described
by elliptic PDE with highly oscillated coefficients.
The homogenization is said to be a process of finding
such homogeneous coefficients that a solution of
original PDE can be approximated by the solution of the
same PDE, but with these new homogeneous coefficients
instead of old highly oscillated coefficients.
Computation of homogenized coefficients of composites
with periodic structure reduces to solving a series of
periodic boundary value problem for the original PDE in
the domain, called cell, of periodicity. For composites
of essentially different components the coefficients of
the PDE in the domain of periodicity are discontinuous
and have big jumps. Another important source of PDE
with jumps of coefficients is Fictitious Domain Method.
In this method the original boundary value problem for
PDE is changed for a new boundary value problem in a
domain that covers the original one. In the new
fictitious part of the domain the coefficients of PDE
are chosen about zero for {Neumann} original boundary
conditions or very large for {Dirichlet} original
boundary conditions, such that a solution of the new
problem approximates or, even, coincides with the
desired solution. Therefore, the fictitious domain
methods makes possible to ``improve'' the shape of the
original boundary, but leads to a PDE with very large
jumps of coefficients. We consider here a nonstandard
variant of the fictitious domain method, namely, with
periodic boundary conditions on the fictitious
boundary. For this variant the problem produced by the
fictitious domain method looks exactly like a problem
produced by the homogenization procedure we were
talking about, i.e., that is a periodic boundary value
problem in a cube for elliptic PDE with discontinuous
coefficients that can achieve, in limit cases, zero or
infinitely large values. There are several different
difficulties associated with numerical solution of
those problems. In the present paper we consider only
one of them, concerned with the rate of convergence of
preconditioned iterative methods. It is well known,
that, typically, the larger is the jumps of
coefficient, the slower is the convergence. Our main
goal is to prove, that with a special initial guess the
rate of convergence does not depend on the value of the
jumps. We do not touch here the mesh approximations of
our PDE, but we can expect that for some natural types
of approximations all our results still hold and the
rate of convergence does not depend of the mesh size
parameter as well. The central idea of the proof is
that with the special initial guess errors of all
iterative steps belong to a subspace and in this
subspace our problem is well posed independently of the
jumps of coefficients. We also consider some related
questions, e.g., the dependence of the solution of
small coefficients in a subdomain",
}
@Article{Balagurov:1983:ICP,
author = "B. Ya. Balagurov",
title = "Isomorphism of certain problems of percolation
theory",
journal = j-Z-EKSP-TEOR-FIZ,
volume = "85",
number = "2",
pages = "568--584",
year = "1983",
CODEN = "ZETFA7",
ISSN = "0044-4510",
fjournal = "Akademiya Nauk SSSR. Zhurnal Eksperimentalnoy i
Teoreticheskoy Fiziki",
}
@Article{Balk:1998:DSN,
author = "A. Balk and A. V. Cherkaev and L. I. Slepyan",
title = "Dynamics of solids with non-monotone stress-strain
relation",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "submitted",
year = "1999",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Ball:1976:CCE,
author = "John M. Ball",
title = "Convexity conditions and existence theorems in
nonlinear elasticity",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "63",
number = "4",
pages = "337--403",
year = "1976/77",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Ball:1981:NLW,
author = "J. M. Ball and J. C. Currie and P. J. Oliver",
title = "Null-Lagrangians, weak continuity, and variational
problems of arbitrary order",
journal = j-J-FUNCT-ANAL,
volume = "41",
number = "",
pages = "4989--5003",
year = "1981",
CODEN = "JFUAAW",
ISSN = "0022-1236",
}
@Article{Ball:1984:QVP,
author = "J. M. Ball and F. Murat",
title = "${W}\sp{1,p}$-quasiconvexity and variational problems
for multiple integrals",
journal = j-J-FUNCT-ANAL,
volume = "58",
number = "3",
pages = "225--253",
year = "1984",
CODEN = "JFUAAW",
ISSN = "0022-1236",
note = "See errata \cite{Ball:1986:EQV}",
fjournal = "Journal of Functional Analysis",
}
@Article{Ball:1986:EQV,
author = "J. M. Ball and F. Murat",
title = "Erratum: ``${W}\sp{1,p}$-quasiconvexity and
variational problems for multiple integrals''",
journal = j-J-FUNCT-ANAL,
volume = "66",
number = "3",
pages = "439",
year = "1986",
CODEN = "JFUAAW",
ISSN = "0022-1236",
fjournal = "Journal of Functional Analysis",
}
@Article{Ball:1987:FPM,
author = "J. M. Ball and R. James",
title = "Finite phase mixtures as minimizers of energy",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "100",
pages = "13--52",
year = "1987",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Ball:1989:RCB,
author = "J. M. Ball and F. Murat",
title = "Remarks on {Chacon}'s biting lemma",
journal = j-PROC-AM-MATH-SOC,
volume = "107",
number = "3",
pages = "655--663",
year = "1989",
CODEN = "PAMYAR",
ISSN = "0002-9939",
fjournal = "Proceedings of the American Mathematical Society",
}
@InCollection{Ball:1989:VFT,
author = "J. M. Ball",
booktitle = "PDEs and continuum models of phase transitions (Nice,
1988)",
title = "A version of the fundamental theorem for {Young}
measures",
volume = "344",
publisher = pub-SV,
address = "Berlin; New York",
pages = "207--215",
year = "1989",
series = "Lecture Notes in Phys.",
}
@InCollection{Ball:1991:RRO,
author = "J. M. Ball and F. Murat",
booktitle = "Ordinary and partial differential equations, Vol. III
(Dundee, 1990)",
title = "Remarks on rank-one convexity and quasiconvexity",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "25--37",
year = "1991",
}
@Article{Ball:1992:PET,
author = "J. M. Ball and R. James",
title = "Proposed experimental tests of a theory of fine
microstructure and two-well problem",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "338A",
pages = "389--450",
year = "1992",
CODEN = "PTRSAV",
ISSN = "0370-2316",
}
@InCollection{Ball:RRO:RRO,
author = "J. M. Ball and F. Murat",
booktitle = "Ordinary and partial differential equations, Vol. III
(Dundee, 1990)",
title = "Remarks on rank-one convexity and quasiconvexity",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "25--37",
year = "1991",
}
@Book{Bandle:1980:IIA,
author = "C. Bandle",
title = "Isoperimetric inequalities and applications",
publisher = "Pitman (Advanced Publishing Program)",
address = "Boston, Mass.",
pages = "x + 228",
year = "1980",
ISBN = "0-273-08423-2",
}
@Article{Banichuk:1977:COP,
author = "N. V. Banichuk",
title = "Conditions of optimality in the problem of finding
shapes of holes in elastic bodies",
journal = j-PRIKL-MAT-MEH,
volume = "41",
number = "5",
pages = "920--925",
year = "1977",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Banichuk:1984:OPE,
author = "N. V. Banichuk and V. G. Bel{\cprime}ski{\u\i} and V.
V. Kobelev",
title = "Optimization in problems of elasticity with unknown
boundaries",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "19",
number = "3",
pages = "46--52",
year = "1984",
CODEN = "IZMTB9",
ISSN = "0572-3299",
fjournal = "Izvestiya Akademii Nauk SSSR. Mekhanika Tverdogo
Tela",
}
@Article{Banichuk:1989:DAS,
author = "N. V. Banichuk and A. S. Bratus{\cprime} and A. D.
Myshkis",
title = "Destabilizing action of small dissipative forces on
nonconservative systems",
journal = j-DOKL-AKAD-NAUK,
volume = "309",
number = "6",
pages = "1325--1327",
year = "1989",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRnumber = "MR91k:70020",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Banichuk:1989:OSE,
author = "N. V. Banichuk and A. S. Bratus{\cprime}",
title = "Optimization of the stability of elastic
nonconservative systems",
journal = j-PRIKL-PROBLEMY-PROCH-I-PLAST,
number = "42",
pages = "11--17 (1990)",
year = "1989",
ISSN = "0132-7186",
MRnumber = "MR91k:73080",
fjournal = "Gor\cprime kovski\u\i\ Gosudarstvenny\u\i\ Universitet
imeni N. I. Lobachevskogo. Prikladnye Problemy
Prochnosti i Plastichnosti",
}
@Article{Barabanov:1993:LLA,
author = "O. O. Barabanov and V. V. Zhikov",
title = "Limit load and averaging",
journal = j-IZV-ROSS-AKAD-NAUK-SER-MAT,
volume = "57",
number = "5",
pages = "15--43",
year = "1993",
ISSN = "0373-2436",
MRnumber = "MR94k:73080",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Izvestiya. Seriya
Matematicheskaya",
}
@Article{Barles:1995:UMP,
author = "G. Barles and F. Murat",
title = "Uniqueness and the maximum principle for quasilinear
elliptic equations with quadratic growth conditions",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "133",
number = "1",
pages = "77--101",
year = "1995",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Barnett:1974:SEC,
author = "D. M. Barnett and J. K. Lee and H. I. Aaronson and K.
C. Russel",
title = "The strain energy of a coherent ellipsoidal
precipitate",
journal = j-SCR-METALL,
volume = "8",
pages = "1447--1450",
year = "1974",
CODEN = "SCRMBU",
ISSN = "0036-9748",
}
@InCollection{Barrett:1996:BEP,
author = "K. E. Barrett and D. R. S. Talbot",
booktitle = "Continuum models and discrete systems (Varna, 1995)",
title = "Bounds for the effective properties of a nonlinear
two-phase composite dielectric",
publisher = "World Sci. Publishing",
address = "River Edge, NJ",
pages = "92--99",
year = "1996",
}
@Article{Begue:1987:NES,
author = "C. B{\`e}gue and C. Conca and F. Murat and O.
Pironneau",
title = "{\`A} nouveau sur les {\'e}quations de {Stokes} et de
{Navier-Stokes} avec des conditions aux limites sur la
pression",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "304",
number = "1",
pages = "23--28",
year = "1987",
CODEN = "CHASAP",
ISSN = "0249-6291",
fjournal = "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
Sciences. S{\'e}rie I. Math{\'e}matique",
}
@InCollection{Begue:1988:ESN,
author = "C. B{\`e}gue and C. Conca and F. Murat and O.
Pironneau",
booktitle = "Nonlinear partial differential equations and their
applications. Coll{\`e}ge de France Seminar, Vol.\ IX
(Paris, 1985--1986)",
title = "Les \'equations de {Stokes} et de {Navier-Stokes} avec
des conditions aux limites sur la pression",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "179--264",
year = "1988",
}
@Article{Beliaev:1996:DER,
author = "A. Yu. A. Beliaev and S. M. Kozlov",
title = "Darcy equation for random porous media",
journal = j-COMM-PURE-APPL-MATH,
volume = "49",
number = "1",
pages = "1--34",
year = "1996",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Ben-Tal:1993:NMO,
author = "A. Ben-Tal and M. P. Bend\-s{\o}e",
fullauthor = "Aharon Ben-Tal and M. P. Bend\-s{\o}e",
title = "A new method for optimal truss topology design",
journal = j-SIAM-J-OPT,
volume = "3",
number = "2",
pages = "322--358",
year = "1993",
CODEN = "SJOPE8",
ISSN = "1052-6234",
fjournal = "SIAM Journal on Optimization",
}
@Article{Bendsoe:1981:EOS,
author = "M. P. Bend\-s{\o}e",
title = "On the existence of observable single-output systems
of a simple type",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "19",
number = "4",
pages = "555--559",
year = "1981",
CODEN = "SJCODC",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Control and Optimization",
}
@InProceedings{Bendsoe:1982:SSM,
author = "M. P. Bend\-s{\o}e",
editor = "E. Atrek and R. H. Gallagher and K. M. Ragsdell and O.
C. Zienkeiwicz",
booktitle = "New Directions in optimal structural design",
title = "Some Smear-out Models for Integrally Stiffened
Plates",
publisher = "Pineridge Press Ltd.",
address = "Swansea",
pages = "{(13--29)}-{(13--34)}",
year = "1982",
}
@InCollection{Bendsoe:1983:CHP,
author = "M. P. Bend\-s{\o}e",
booktitle = "Optimization methods in structural design (Siegen,
1982)",
title = "${G}$-closure and homogenization problems arising in
plate optimization",
publisher = "Bibliographisches Inst.",
address = "Mannheim",
pages = "270--275",
year = "1983",
}
@Article{Bendsoe:1983:VFM,
author = "M. P. Bend\-s{\o}e and N. Olhoff and J. E. Taylor",
title = "A Variational Formulation for Multicriteria Structural
Optimization",
journal = j-J-STRUCT-MECH,
volume = "11",
number = "",
pages = "523--544",
year = "1983",
CODEN = "JSMHA2",
ISSN = "0360-1218",
}
@InCollection{Bendsoe:1984:EPC,
author = "M. P. Bend\-s{\o}e",
booktitle = "System modelling and optimization (Copenhagen, 1983)",
title = "Existence proofs for a class of plate optimization
problems",
publisher = pub-SV,
address = "Berlin",
pages = "773--779",
year = "1984",
}
@Article{Bendsoe:1985:MDA,
author = "M. P. Bend\-s{\o}e and N. Olhoff",
title = "A method of design against vibration resonance of
beams and shafts",
journal = j-OPT-CTL-APPL-METH,
volume = "6",
number = "3",
pages = "191--200",
year = "1985",
CODEN = "OCAMD5",
ISSN = "0143-2087",
fjournal = "Optimal Control Applications \& Methods",
}
@Article{Bendsoe:1985:SAP,
author = "M. P. Bend\-s{\o}e and N. Olhoff and J.
Soko{\l}owski",
title = "Sensitivity analysis of problems of elasticity with
unilateral constraints",
journal = j-J-STRUCT-MECH,
volume = "13",
number = "2",
pages = "201--222",
year = "1985",
CODEN = "JSMHA2",
ISSN = "0360-1218",
fjournal = "Journal of Structural Mechanics",
}
@InProceedings{Bendsoe:1986:GPM,
author = "M. P. Bend\-s{\o}e",
editor = "",
booktitle = "Homogenization and Effective Moduli of Materials and
Media (Minneapolis, Minn., 1984/1985)",
title = "Generalized Plate Models and Optimal Design",
organization = "",
publisher = pub-SV,
address = "Berlin; New York",
pages = "1--26",
month = "",
year = "1986",
}
@Article{Bendsoe:1987:DSCa,
author = "M. P. Bend\-s{\o}e and N. Olhoff and J. E. Taylor",
title = "On the design of structure and controls for optimal
performance of actively controlled flexible
structures",
journal = j-MECHAN-STRUCT-MACH,
volume = "15",
number = "3",
pages = "265--295",
year = "1987",
CODEN = "MSMAEI",
ISSN = "0890-5452",
fjournal = "Mechanics of Structures and Machines. An International
Journal",
}
@InCollection{Bendsoe:1987:DSCb,
author = "M. P. Bend\-s{\o}e",
booktitle = "Computer aided optimal design: structural and
mechanical systems (Tr{\'o}ia, 1986)",
title = "Design of structure and controllers for optimal
performance",
publisher = pub-SV,
address = "Berlin",
pages = "181--193",
year = "1987",
}
@Article{Bendsoe:1987:SAO,
author = "M. P. Bend\-s{\o}e and J. Soko{\l}owski",
title = "Sensitivity analysis and optimal design of elastic
plates with unilateral point supports",
journal = j-MECHAN-STRUCT-MACH,
volume = "15",
number = "3",
pages = "383--393",
year = "1987",
CODEN = "MSMAEI",
ISSN = "0890-5452",
fjournal = "Mechanics of Structures and Machines. An International
Journal",
}
@Article{Bendsoe:1988:DSA,
author = "M. P. Bend\-s{\o}e and J. Soko{\l}owski",
title = "Design sensitivity analysis of elastic-plastic
analysis problems",
journal = j-MECHAN-STRUCT-MACH,
volume = "16",
number = "1",
pages = "81--102",
year = "1988",
CODEN = "MSMAEI",
ISSN = "0890-5452",
fjournal = "Mechanics of Structures and Machines. An International
Journal",
}
@Article{Bendsoe:1988:GOT,
author = "M. P. Bend\-s{\o}e and N. Kikuchi",
title = "Generating Optimal Topologies in Structural Design
using a Homogenization Method",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "71",
number = "2",
pages = "197--224",
year = "1988",
CODEN = "CMMECC",
ISSN = "0045-7825",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
}
@InCollection{Bendsoe:1988:ODA,
author = "M. P. Bend\-s{\o}e",
booktitle = "Boundary control and boundary variations (Nice,
1986)",
title = "On optimal design of actively controlled distributed
parameter structures",
publisher = pub-SV,
address = "Berlin",
pages = "55--71",
year = "1988",
}
@Article{Bendsoe:1989:OSD,
author = "M. P. Bend\-s{\o}e",
title = "Optimal Shape Design as a Material Distribution
Problem",
journal = j-STRUCT-OPTIM,
volume = "1",
number = "",
pages = "193--202",
year = "1989",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Bendsoe:1990:TBV,
author = "M. P. Bend\-s{\o}e and H. C. Rodrigues",
title = "On topology and boundary variations in shape
optimization",
journal = j-CONTROL-CYBERN,
volume = "19",
number = "3-4",
pages = "9--26",
year = "1990",
CODEN = "CCYBAP",
ISSN = "0324-8569",
note = "Optimal design and control of structures (Jab\l onna,
1990).",
fjournal = "Polish Academy of Sciences. Systems Research
Institute. Control and Cybernetics",
xxyear = "1991",
}
@Article{Bendsoe:1991:ITB,
author = "M. P. Bend\-s{\o}e and H. Carrico Rodrigues",
fullauthor = "M. P. Bend\-s{\o}e and Helder Carrico Rodrigues",
title = "Integrated topology and boundary shape optimization of
$2${D} solids",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "87",
number = "1",
pages = "15--34",
year = "1991",
CODEN = "CMMECC",
ISSN = "0045-7825",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
}
@InCollection{Bendsoe:1993:TGL,
author = "M. P. Bend\-s{\o}e and A. R. D{\'\i}az and N.
Kikuchi",
booktitle = "Topology design of structures (Sesimbra, 1992)",
title = "Topology and generalized layout optimization of
elastic structures",
publisher = pub-KLUWER,
address = "Dordrecht",
pages = "159--205",
year = "1993",
}
@InProceedings{Bendsoe:1993:TOG,
author = "M. P. Bend\-s{\o}e and A. R. D{\'\i}az and N.
Kikuchi",
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "{Topology Design} of {Structures}, {Sesimbra,
Portugal}",
title = "Topology Optimization and Generalized Layout
Optimization of Elastic Structures",
organization = "NATO ASI",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "159--205",
month = "",
year = "1993",
}
@InCollection{Bendsoe:1993:TTO,
author = "M. P. Bend\-s{\o}e and A Ben-Tal",
fullauthor = "M. P. Bend\-s{\o}e and Aharon Ben-Tal",
booktitle = "Optimization of large structural systems, Vol.\ I, II
(Berchtesgaden, 1991)",
title = "Truss topology optimization by a displacements based
optimality criterion approach",
publisher = pub-KLUWER,
address = "Dordrecht",
pages = "139--155",
year = "1993",
}
@Article{Bendsoe:1994:AMP,
author = "M. P. Bend\-s{\o}e and J. M. Guedes and R. B. Haber
and P. Pedersen and J. E. Taylor",
title = "An analytical model to predict optimal material
properties in the context of optimal structural
design",
journal = j-J-APPL-MECH,
volume = "61",
number = "4",
pages = "930--937",
year = "1994",
CODEN = "JAMCAV",
ISSN = "0021-8936",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Journal of Applied Mechanics",
}
@Article{Bendsoe:1994:SCA,
author = "M. P. Bend\-s{\o}e and J. M. Guedes",
title = "Some computational aspects of using extremal material
properties in the optimal design of shape, topology and
material",
journal = j-CONTROL-CYBERN,
volume = "23",
number = "3",
pages = "327--349",
year = "1994",
CODEN = "CCYBAP",
ISSN = "0324-8569",
note = "Shape design and optimization.",
fjournal = "Control and Cybernetics",
}
@InCollection{Bendsoe:1995:MCD,
author = "M. P. Bend\-s{\o}e and V. B. Hammer and R. Lipton and
P. Pedersen",
booktitle = "Homogenization and applications to material sciences
(Nice, 1995)",
title = "Minimum compliance design of laminated plates",
publisher = "Gakk\=otosho",
address = "Tokyo",
pages = "45--56",
year = "1995",
note = "see also \cite{Bendsoe:1996:PLD}",
}
@Article{Bendsoe:1995:ODM,
author = "M. P. Bend\-s{\o}e and A. R. D{\'\i}az and R. Lipton
and J. E. Taylor",
title = "Optimal design of material properties and material
distribution for multiple loading conditions",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "38",
number = "7",
pages = "1149--1170",
year = "1995",
CODEN = "IJNMBH",
ISSN = "0029-5981",
fjournal = "International Journal for Numerical Methods in
Engineering",
}
@Book{Bendsoe:1995:OST,
author = "M. P. Bend\-s{\o}e",
editor = "",
title = "Optimization of Structural Topology, Shape, and
Material",
volume = "",
publisher = pub-SV,
address = pub-SV:adr,
edition = "",
pages = "xii + 271",
month = "",
year = "1995",
ISBN = "3-540-59057-9",
series = "",
}
@Article{Bendsoe:1995:SSAa,
author = "M. P. Bend\-s{\o}e and J. Soko{\l}owski",
title = "Shape sensitivity analysis of optimal compliance
functionals",
journal = j-MECHAN-STRUCT-MACH,
volume = "23",
number = "1",
pages = "35--58",
year = "1995",
CODEN = "MSMAEI",
ISSN = "0890-5452",
fjournal = "Mechanics of Structures and Machines. An International
Journal",
}
@InCollection{Bendsoe:1995:SSAb,
author = "M. P. Bend\-s{\o}e and J. Soko{\l}owski",
booktitle = "Recent developments in optimization (Dijon, 1994)",
title = "Shape sensitivity analysis of nonsmooth shape
functionals",
publisher = pub-SV,
address = "Berlin",
pages = "36--45",
year = "1995",
}
@Article{Bendsoe:1996:OSMa,
author = "M. P. Bend\-s{\o}e and J. M. Guedes and S. Plaxton and
J. E. Taylor",
title = "Optimization of structure and material properties for
solids composed of softening material",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "33",
number = "12",
pages = "1799--1813",
year = "1996",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@InCollection{Bendsoe:1996:OSMb,
author = "M. P. Bend\-s{\o}e and J. M. Guedes and S. Plaxton and
J. E. Taylor",
booktitle = "IUTAM Symposium on Optimization of Mechanical Systems
(Stuttgart, 1995)",
title = "Optimization of structure \& material properties for
solids composed of softening material",
publisher = pub-KLUWER,
address = "Dordrecht",
pages = "17--24",
year = "1996",
}
@Article{Bendsoe:1996:PLD,
author = "M. P. Bend\-s{\o}e and A. R. D{\'\i}az and R. Lipton
and J. E. Taylor",
title = "Parametrization in Laminate Design for Optimal
Compliance",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "34",
pages = "415--434",
year = "1996",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Bendsoe:1997:EOE,
author = "M. P. Bend\-s{\o}e and R. Lipton",
title = "Extremal overall elastic response of polycrystalline
materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "11-12",
pages = "1765--1780",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Book{Bensoussan:1978:AAP,
author = "A. Bensoussan and J. L. Lions and G. Papanicolaou",
title = "Asymptotic analysis of periodic structures",
publisher = "North-Holland Publ.",
year = "1978",
}
@Article{Bensoussan:1986:HEE,
author = "A. Bensoussan and L. Boccardo and F. Murat",
title = "Homogenization of elliptic equations with principal
part not in divergence form and {Hamiltonian} with
quadratic growth",
journal = j-COMM-PURE-APPL-MATH,
volume = "39",
number = "6",
pages = "769--805",
year = "1986",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Bensoussan:1988:NPD,
author = "A. Bensoussan and L. Boccardo and F. Murat",
title = "On a nonlinear partial differential equation having
natural growth terms and unbounded solution",
journal = j-ANN-INST-HENRI-POINCARE-ANAL-NON-LINEAIRE,
volume = "5",
number = "4",
pages = "347--364",
year = "1988",
ISSN = "0294-1449",
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Analyse Non
Lin{\'e}aire",
}
@TechReport{Bensoussan:1990:HCQ,
author = "A. Bensoussan and L. Boccardo and F. Murat",
title = "{H-convergence} for quasilinear elliptic equations
with quadratic growth",
institution = "Publication du Laboratoire d'Analyse Num{\'e}rique,
Universit{\'e} Pierre et Marie Curie",
year = "1990",
abstract = "In this paper we consider the problem ?? hier
fehlen Zeilen - ein equation/array where the matrices
$a^\epsilon (x)$ converge in the sense of
homogenization, where $\gamma \ge 0$ and where the
Hamiltonians $H^\epsilon$ satisfy
\setcounter{equation}{1} \begin{equation} \mid
H^\epsilon (x, s, \xi) \mid \le c_0 + b (\mid s \mid)
\mid \xi \mid^2 \end{equation} (with $c_0$ a constant
and $b(s)$ a nondecreasing function). We prove that
extracting a subsequence, $u^{\epsilon'}$ converges
weakly * in $H{_{0}^{1}} (\Omega) \cap L^\infty
(\Omega)$ to the solution of a problem similar to (1),
the Hamiltonian of which is given by
\setcounter{equation}{2} \begin{equation} H(x, s, \xi)
= lim_{D'(\Omega)} H^{\epsilon'}(x,s,P^{\epsilon'}(x)
\xi); \end{equation} here the matrices $P^\epsilon$ are
the corrector matrices of the linear problem, which we
assume to be bounded in $(L^\infty (\Omega))^{N^2}$. We
also consider the problem (?? hier fehlt equation3)
where the matrices $a^\epsilon(x)$ are now supposed to
be symmetric and still to converge in the sense of
homogenization; here $f$ belongs to $H^{-1}(\Omega)$
while further to (2), $G^\epsilon$ satisfies the sign
condition $s G^\epsilon (x, s, \xi) \ge 0$ and a growth
condition with respect to $s$. Under these hypotheses
we prove again that extracting a subsequence,
$v^{\epsilon'}$ converges weakly in
$H{{_0}{^1}}(\Omega)$ to the solution of a problem
similar to (4). In contrast with (1), the solution
$v^\epsilon$ of (4) is no more bounded in
$L^\infty(\Omega)$, which gives extra difficulties in
the homogenization process.",
}
@Article{Bensoussan:1992:CQL,
author = "A. Bensoussan and L. Boccardo and F. Murat",
title = "${H}$ convergence for quasi-linear elliptic equations
with quadratic growth",
journal = j-APPL-MATH-OPTIM,
volume = "26",
number = "3",
pages = "253--272",
year = "1992",
CODEN = "AMOMBN",
ISSN = "0095-4616",
fjournal = "Applied Mathematics and Optimization. An International
Journal",
}
@InCollection{Bensoussan:1992:HNP,
author = "A. Bensoussan and L. Boccardo and F. Murat",
booktitle = "Progress in partial differential equations: calculus
of variations, applications (Pont-\`a-Mousson, 1991)",
title = "Homogenization of a nonlinear partial differential
equation with unbounded solution",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "1--12",
year = "1992",
}
@InProceedings{Benveniste:1990:CBM,
author = "Y. Benveniste and G. J. Dvorak",
editor = "G. Weng and others",
booktitle = "Micromechanics and Inhomogeneity",
title = "On correspondence between mechanical and thermal
effects in two-phase composites",
publisher = pub-SV,
address = pub-SV:adr,
pages = "65--80",
year = "1990",
}
@Article{Benveniste:1991:DES,
author = "Y. Benveniste and G. J. Dvorak and T. Chen",
title = "On diagonal and elastic symmetry of the approximate
effective stiffness tensor of heterogeneous media",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "39",
number = "7",
pages = "927--946",
year = "1991",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR92i:73084",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Benveniste:1992:UFU,
author = "Y. Benveniste and G. J. Dvorak",
title = "Uniform fields and universal relations in
piezoelectric composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "40",
number = "6",
pages = "1295--1312",
year = "1992",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR93g:73101",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Benveniste:1993:ERM,
author = "Y. Benveniste",
title = "Exact results in the micromechanics of fibrous
piezoelectric composites exhibiting pyroelectricity",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "441",
pages = "59--81",
year = "1993",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@Article{Benveniste:1993:URPa,
author = "Y. Benveniste",
title = "Universal relations in piezoelectric composites with
eigenstress and polarization fields. {I}. {Binary}
media---local fields and effective behavior",
journal = j-J-APPL-MECH,
volume = "60",
number = "2",
pages = "265--269",
year = "1993",
CODEN = "JAMCAV",
ISSN = "0021-8936",
MRnumber = "MR94g:73037a",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Journal of Applied Mechanics",
}
@Article{Benveniste:1993:URPb,
author = "Y. Benveniste",
title = "Universal relations in piezoelectric composites with
eigenstress and polarization fields. {II}. {Multiphase}
media---effective behavior",
journal = j-J-APPL-MECH,
volume = "60",
number = "2",
pages = "270--275",
year = "1993",
CODEN = "JAMCAV",
ISSN = "0021-8936",
MRnumber = "MR94g:73037b",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Journal of Applied Mechanics",
}
@Article{Benveniste:1994:ECB,
author = "Y. Benveniste",
title = "Exact connections between polycrystal and crystal
properties in two-dimensional polycrystalline
aggregates",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "447",
pages = "1--22",
year = "1994",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@Article{Benveniste:1995:CRA,
author = "Y. Benveniste",
title = "Correspondence relations among equivalent classes of
heterogeneous piezoelectric solids under anti-plane
mechanical and in-plane electrical fields",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "43",
number = "4",
pages = "553--571",
year = "1995",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR97b:73003",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Benveniste:1996:TEP,
author = "Y. Benveniste",
title = "Thermal expansion of polycrystalline aggregates
consisting of elongated crystals and containing
cylindrical pores or inclusions",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "44",
number = "1",
pages = "137--153",
year = "1996",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR96h:73005",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Beran:19xx:BEC,
author = "M. J. Beran and P. A. Mason and B. Adams and T.
Olsen",
title = "Bounding elastic constants of an orthotropic
polycrystal using measurements of the microstructure",
journal = j-J-MECH-PHYS-SOLIDS,
year = "19xx",
CODEN = "JMPSA8",
ISSN = "0022-5096",
note = "Submitted.",
}
@Book{Berdichevsky:1983:VPC,
author = "V. Berdichevsky",
title = "Variational principles of continuum mechanics",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
year = "1983",
note = "In {Russian}.",
}
@Article{Berdichevsky:1991:NTV,
author = "V. Berdichevsky and I. Kunin and F. Hussain",
title = "Negative temperature of vortex motion",
journal = j-PHYS-REV-A,
volume = "43",
number = "4",
pages = "2050--2051",
year = "1991",
CODEN = "PLRAAN",
ISSN = "1050-2947",
fjournal = "Physical Review. A. General Physics. Third Series",
}
@Book{Berdichevsky:1997:TCO,
author = "V. Berdichevsky",
title = "Thermodynamics of chaos and order",
publisher = "Longman",
address = "Harlow",
pages = "x + 267",
year = "1997",
ISBN = "0-582-08734-1",
}
@Book{Berdichevsky:1999:H,
editor = "V. Berdichevsky and V. Jikov and G. Papanicolaou",
title = "Homogenization",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
year = "1999",
ISBN = "",
LCCN = "",
}
@Article{Berger:1970:ASN,
author = "M. S. Berger and L. E. Fraenkel",
title = "On the asymptotic solution of a nonlinear {Dirichlet}
problem",
journal = j-J-MATH-MECH,
volume = "19",
number = "7",
pages = "553--585",
year = "1970",
CODEN = "JOMMAN",
ISSN = "0095-9057",
}
@Article{Bergman:1977:CBC,
author = "D. J. Bergman and Y. Imry",
title = "Critical behavior of the complex dielectric constant
near the percolation threshold of a heterogeneous
material",
journal = j-PHYS-REV-LET,
volume = "39",
pages = "1222--1225",
year = "1977",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Bergman:1978:DCC,
author = "D. J. Bergman",
title = "The dielectric constant of a composite material---a
problem in classical physics",
journal = j-PHYS-REP,
volume = "43",
number = "9",
pages = "377--407",
year = "1978",
CODEN = "PRPLCM",
ISSN = "0370-1573",
MRnumber = "MR58:14402",
}
@Article{Bergman:1980:ESM,
author = "D. J. Bergman",
title = "Exactly solvable microscopic geometries and rigorous
bounds for the complex dielectric constant of a
two-component composite material",
journal = j-PHYS-REV-LET,
volume = "44",
pages = "1285--1287",
year = "1980",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Bergman:1982:RBC,
author = "D. J. Bergman",
title = "Rigorous bounds for the complex dielectric constant of
a two-component composite",
journal = j-ANN-PHYS,
volume = "138",
number = "1",
pages = "78--114",
year = "1982",
CODEN = "APNYA6",
ISSN = "0003-4916",
MRnumber = "MR84e:78006",
fjournal = "Annals of Physics",
}
@Article{Bergman:1984:CPE,
author = "D. J. Bergman and Y. Kantor",
fullauthor = "D. J. Bergman and Yacov Kantor",
title = "Critical properties of an elastic fractal",
journal = j-PHYS-REV-LET,
volume = "53",
number = "6",
pages = "511--514",
year = "1984",
CODEN = "PRLTAO",
ISSN = "0031-9007",
MRnumber = "MR85g:82061",
fjournal = "Physical Review Letters",
}
@InCollection{Bergman:1985:BPP,
author = "D. Bergman",
booktitle = "Homogenization methods: theory and applications in
physics (Br{\'e}au-sans-Nappe, 1983)",
title = "Bulk physical properties of composite media",
publisher = pub-EYROLLES,
address = pub-EYROLLES:adr,
pages = "1--128",
year = "1985",
MRnumber = "MR844870",
}
@InCollection{Bergman:1986:EDC,
author = "D. J. Bergman",
booktitle = "Homogenization and effective moduli of materials and
media (Minneapolis, Minn., 1984/1985)",
title = "The effective dielectric coefficient of a composite
medium: rigorous bounds from analytic properties",
publisher = pub-SV,
address = "New York",
pages = "27--51",
year = "1986",
MRnumber = "MR87j:78005",
}
@InCollection{Bergman:1991:EMA,
author = "D. J. Bergman",
booktitle = "Composite media and homogenization theory (Trieste,
1990)",
title = "Effective medium approximation for nonlinear
conductivity of a composite medium",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "67--79",
year = "1991",
MRnumber = "MR92i:78006",
}
@Article{Bergman:1992:PPM,
author = "D. J. Bergman and D. Stroud",
title = "Physical Properties of Macroscopically Inhomogeneous
Media",
journal = j-SOLID-STATE-PHYS-N-Y-1955,
volume = "46",
pages = "147--269",
year = "1992",
CODEN = "SSPHAE",
ISSN = "0081-1947",
}
@InCollection{Bergman:1996:NBC,
author = "D. J. Bergman",
booktitle = "Continuum models and discrete systems (Varna, 1995)",
title = "Nonlinear behavior in a composite medium: the
importance of resonances and percolation",
publisher = "World Sci. Publishing",
address = "River Edge, NJ",
pages = "111--117",
year = "1996",
MRnumber = "MR1442963",
}
@Article{Berlyand:1994:ERE,
author = "L. Berlyand and K. Golden",
title = "Exact result for the effective conductivity of a
continuum percolation model",
journal = j-PHYS-REV-B,
volume = "50",
pages = "2114--2117",
year = "1994",
CODEN = "PLRBAQ",
ISSN = "0556-2805",
bibdate = "Fri Dec 30 10:52:44 1994",
}
@Article{Berryman:1988:MRC,
author = "J. G. Berryman and G. W. Milton",
title = "Microgeometry of random composites and porous media",
journal = j-J-PHYS-D,
volume = "21",
pages = "87--94",
year = "1988",
CODEN = "JPAPBE",
ISSN = "0022-3727",
}
@Article{Bhattacharya:1993:CGN,
author = "K. Bhattacharya",
title = "Comparison of the geometrically nonlinear and linear
theories of martensitic transformation",
journal = j-CONTIN-MECH-THERMODYN,
volume = "5",
pages = "205--242",
year = "1993",
CODEN = "CMETEJ",
ISSN = "0935-1175",
}
@Article{Bhattacharya:1994:RM,
author = "K. Bhattacharya and N. B. Firoozye and R. D. James and
R. V. Kohn",
title = "Restrictions on microstructure",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "124",
number = "5",
pages = "843--878",
year = "1994",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Bhattacharya:1997:EEM,
author = "K. Bhattacharya and R. V. Kohn",
title = "Elastic energy minimization and the recoverable
strains of polycrystalline shape-memory materials",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "139",
pages = "99--180",
year = "1997",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Book{Biedenharn:1981:AMQ,
author = "L. C. Biedenharn and J. D. Louck",
title = "Angular momentum in quantum physics",
volume = "8",
publisher = "Addison-Wesley Publishing Co., Reading, Mass.",
pages = "xxxii + 716",
year = "1981",
ISBN = "0-201-13507-8",
note = "Theory and application, with a foreword by Peter A.
Carruthers.",
series = "Encyclopedia of Mathematics and its Applications",
}
@Article{Blanchard:1997:RSN,
author = "D. Blanchard and F. Murat",
title = "Renormalised solutions of nonlinear parabolic problems
with ${L}\sp1$ data: existence and uniqueness",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "127",
number = "6",
pages = "1137--1152",
year = "1997",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Book{Bliss:1946:LCV,
author = "G. A. Bliss",
fullauthor = "Gilbert A. Bliss",
title = "Lectures on the Calculus of Variations",
publisher = pub-U-CHICAGO,
address = pub-U-CHICAGO:adr,
pages = "ix + 296",
year = "1946",
}
@Article{Boccardo:1988:EBS,
author = "L. Boccardo and F. Murat and J.-P. Puel",
title = "Existence of bounded solutions for nonlinear elliptic
unilateral problems",
journal = j-ANN-MAT-PURA-APPL-4,
volume = "152",
pages = "183--196",
year = "1988",
CODEN = "ANLMAE",
ISSN = "0003-4622",
fjournal = "Annali di Matematica Pura ed Applicata. Serie Quarta",
}
@Article{Boccardo:1988:QPO,
author = "L. Boccardo and F. Murat and J.-P. Puel",
title = "Quelques propri{\'e}t{\'e}s des op{\'e}rateurs
elliptiques quasi lin{\'e}aires",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "307",
number = "14",
pages = "749--752",
year = "1988",
CODEN = "CASMEI",
ISSN = "0249-6291",
fjournal = "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
Sciences. S{\'e}rie I. Math{\'e}matique",
}
@Article{Boccardo:1989:ERS,
author = "L. Boccardo and F. Murat and J.-P. Puel",
fullauthor = "Lucio Boccardo and F. Murat and J.-P. Puel",
title = "Existence results for some quasilinear parabolic
equations",
journal = j-NONLINEAR-ANAL,
volume = "13",
number = "4",
pages = "373--392",
year = "1989",
CODEN = "NOANDD",
ISSN = "0362-546X",
fjournal = "Nonlinear Analysis",
}
@InProceedings{Boccardo:1989:ESW,
author = "L. Boccardo and J. I. D{\'\i}az and D. Giachetti and
F. Murat",
booktitle = "Recent advances in nonlinear elliptic and parabolic
problems (Nancy, 1988)",
title = "Existence of a solution for a weaker form of a
nonlinear elliptic equation",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "229--246",
year = "1989",
note = "To appear.",
series = "Pitman Research Notes in Ma\-the\-matics Series",
abstract = "Consider the nonlinear elliptic equation
\setcounter{equation}{0} \begin{equation} - div (A \
grad \ u) - div (\phi(u)) = f \ \mbox{in} \ \Omega, u
\in H{_{0}^{1}}(\Omega) \end{equation}, where $A$ is a
${(L^\infty(\Omega))}^{N \times N}$ coercive matrix, $f
\in H{^{-1}}(\Omega)$ and $\phi \in {(C^0(R))}^N$; no
growth restriction is assumed on $\phi$; thus the term
$div (\phi(u))$ cannot be understood in the
distributional sense. In this paper we prove the
existence of a solution of \setcounter{equation}{1}
\begin{equation} [- div (A \ grad \ u)] h(u) - div
(\phi(u) h(u) ) + \phi(u)h'(u) \ grad \ u = f h(u) \
\mbox{in} \ \Omega, \forall h \in C{_{c}^{1}}(\Omega)
\end{equation} where in contrast with (1) every term
has a meaning in $D'(\Omega)$ if $u \in
H{{_0}{^1}}(\Omega)$. Equation (2) is a weaker form of
the original problem, obtained in a formal way through
a pointwise multiplication of (1) by $h(u)$.",
}
@Article{Boccardo:1990:GTH,
author = "L. Boccardo and D. Giachetti and F. Murat",
title = "A generalization of a theorem of {H. Br{\'e}zis} \&
{F. E. Browder} and applications to some unilateral
problems",
journal = j-ANN-INST-HENRI-POINCARE-ANAL-NON-LINEAIRE,
volume = "7",
number = "4",
pages = "367--384",
year = "1990",
ISSN = "0294-1449",
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Analyse Non
Lin{\'e}aire",
}
@InCollection{Boccardo:1991:HNU,
author = "L. Boccardo and F. Murat",
fullauthor = "Lucio Boccardo and F. Murat",
booktitle = "Composite media and homogenization theory (Trieste,
1990)",
title = "Homogenization of nonlinear unilateral problems",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "81--105",
year = "1991",
}
@Article{Boccardo:1992:AEC,
author = "L. Boccardo and F. Murat",
fullauthor = "Lucio Boccardo and F. Murat",
title = "Almost everywhere convergence of the gradients of
solutions to elliptic and parabolic equations",
journal = j-NONLINEAR-ANAL,
volume = "19",
number = "6",
pages = "581--597",
year = "1992",
CODEN = "NOANDD",
ISSN = "0362-546X",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal",
}
@Article{Boccardo:1992:ESN,
author = "L. Boccardo and F. Murat and J.-P. Puel",
title = "${L}\sp\infty$ estimate for some nonlinear elliptic
partial differential equations and application to an
existence result",
journal = j-SIAM-J-MATH-ANA,
volume = "23",
number = "2",
pages = "326--333",
year = "1992",
CODEN = "SJMAAH",
ISSN = "0036-1410",
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Boccardo:1992:USC,
author = "L. Boccardo and T. Gallou{\"e}t and F. Murat",
fullauthor = "Lucio Boccardo and Thierry Gallou{\"e}t and F. Murat",
title = "Unicit{\'e} de la solution de certaines \'equations
elliptiques non lin{\'e}aires",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "315",
number = "11",
pages = "1159--1164",
year = "1992",
CODEN = "CASMEI",
ISSN = "0764-4442",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences.
S{\'e}rie I. Math{\'e}matique",
}
@Article{Boccardo:1993:ERR,
author = "L. Boccardo and D. Giachetti and J. I. D{\'\i}az and
F. Murat",
title = "Existence and regularity of renormalized solutions for
some elliptic problems involving derivatives of
nonlinear terms",
journal = j-J-DIFFER-EQU,
volume = "106",
number = "2",
pages = "215--237",
year = "1993",
CODEN = "JDEQAK",
ISSN = "0022-0396",
fjournal = "Journal of Differential Equations",
}
@InCollection{Boccardo:1993:UPT,
author = "L. Boccardo and T. Gallou{\"e}t and F. Murat",
booktitle = "Progress in partial differential equations: the Metz
surveys, 2 (1992)",
title = "A unified presentation of two existence results for
problems with natural growth",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "127--137",
year = "1993",
}
@Article{Boccardo:1994:PNE,
author = "L. Boccardo and F. Murat",
fullauthor = "Lucio Boccardo and F. Murat",
title = "A property of nonlinear elliptic equations when the
right-hand side is a measure",
journal = j-POTENTIAL-ANAL,
volume = "3",
number = "3",
pages = "257--263",
year = "1994",
CODEN = "POANE2",
ISSN = "0926-2601",
fjournal = "Potential Analysis. An International Journal Devoted
to the Interactions between Potential Theory,
Probability Theory, Geometry and Functional Analysis",
}
@Article{Bohm:1989:WPF,
author = "M. B{\"o}hm",
title = "Well-Posedness of the Fissured-Media Equation",
journal = j-MATH-NACHR,
volume = "140",
pages = "49--58",
year = "1989",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
}
@Article{Borcea:1998:NAT,
author = "L. Borcea and G. Papanicolaou",
title = "Network approximation for transport properties of high
contrast materials",
journal = j-SIAM-J-APPL-MATH,
volume = "58",
number = "2",
pages = "501--539 (electronic)",
year = "1998",
CODEN = "SMJMAP",
ISSN = "1095-712X",
MRnumber = "MR1617638",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Bourgeat:1988:CBH,
author = "A. Bourgeat and M. Quintard and S. Whitaker",
title = "Comparison between homogenization theory and volume
averaging method with closure problem (in {French})",
journal = j-C-R-ACAD-SCI-PARIS,
volume = "S{\'e}rie II",
number = "306",
pages = "463--466",
year = "1988",
abstract = "Various methods have been proposed for obtaining the
macroscopic transport equations starting with the local
transport equations for heterogeneous media. The
results obtained by homogenization theory are compared
to those obtained by the volume averaging method and
closure problem. This comparison is based on the study
of a linear diffusion problem.",
}
@Article{Bourgeat:1993:NHB,
author = "A. Bourgeat and A. Mikeli{\'c}",
title = "A Note on Homogenization of {Bingham} Flow through a
Porous Medium",
journal = j-J-MATH-PURES-APPL,
number = "72",
pages = "405--414",
year = "1993",
CODEN = "JMPAAM",
ISSN = "0021-7824",
abstract = "Homogenization of {Bingham} flow through a porous
medium was considered in the paper J. L. Lions, E.
Sanchez-Palencia: ``Ecoulement d'un fluide
viscoplastique de {Bingham} dans un milieu poreux'', J.
Math. pures et appl., 60, 1981, pp. 341-460, where the
modelling and the formal expansion are presented.
However the convergence of the homogenization process
was left as an open problem. Here we address this issue
and prove the convergence of the process. Thus their
result is not only formal. We use monotonicity methods
coupled with the recently developed notion of two-scale
convergence.",
}
@TechReport{Bourgeat:1994:RRD,
author = "A. Bourgeat and S. Luckhaus and A. Mikeli{\'c}",
fullauthor = "Alain Bourgeat and S. Luckhaus and A. Mikeli{\'c}",
title = "A Rigorous Result for a Double Porosity Model of
Immiscible Two-Phase Flow",
number = "186",
institution = "Equipe d'Analyse Num{\'e}rique Lyon Saint-Etienne,
CNRS URA 740",
year = "1994",
abstract = "In this paper we justify by periodic homogenization
the double porosity model for immiscible incompressible
two-phase flows. The volume fraction of the fissured
part and the nonfissured part are kept positive
constants and of same order. The scaling is such that,
in the final homogenized equations, the less permeable
part of the matrix contributes as a nonlinear memory
term. For the first part of the proof we use the
two-scale convergence as it seems to be appropriate for
the problem, even though to work with periodic
modulation would be possible. The fact that the
equations are nonlinear and degenerated parabolic means
that in the final step of the convergence proof of the
other hand we have to use periodic modulation instead
of two-scale convergence.",
}
@Article{Bourgeat:1995:EET,
author = "A. Bourgeat and S. M. Kozlov and A. Mikeli{\'c}",
title = "Effective equations of two-phase flow in random
media",
journal = j-CALC-VAR-PARTIAL-DIFFER-EQU,
volume = "3",
number = "3",
pages = "385--406",
year = "1995",
ISSN = "0944-2669",
abstract = "We consider the behavior of incompressible two-phase
flow in heterogeneous reservoirs with randomly placed
heterogeneities; that is, in media with permeability
$A$ and porosity $\Phi$ which are stochastically
homogeneous stationary random fields. We assume both
the Darcy velocity and the diffusion flux being given
nonlinear functions of the concentration. Using the
tools of stochastic homogenization we get the nonlinear
effective equations which govern the flow behavior in a
homogeneous medium, being equivalent in the sense of
homogenization theory, to the original one. When
$\epsilon$ is small the randomly heterogeneous porous
medium behaves like a deterministic medium with
effective permeability tensor $A^0$. It is shown how to
calculate the effective permeability tensor $A^0$ by
solving auxiliary stochastic problems. Using the
rescaling parameter $\epsilon$, corresponding to the
characteristic scale of heterogeneities, we prove the
convergence of the homogenization process for $\epsilon
\longrightarrow 0$. Furthermore, by using regularity
results for the nonlinear effective equations we
construct the correctors and establish strong
convergence.",
fjournal = "Calculus of Variations and Partial Differential
Equations",
}
@Article{Bourgeat:19xx:HPF,
author = "A. Bourgeat and A. Mikelic",
title = "Homogenization of a polymer flow through a porous
medium",
journal = j-NONLINEAR-ANAL,
year = "19xx",
CODEN = "NOANDD",
ISSN = "0362-546X",
abstract = "We derive the constitutive laws that connect the
velocity and the pressure gradient in stationary
incompressible purely viscous non-Newtonian flow
through porous media. Starting from the stationary
non-Newtonian Navier-{Stokes} system, with viscosity
obeying Carreau and power laws, and using the
homogenization theory, we obtain a variety of laws
according to the size of Reynolds number. It appears
that there is a critical Reynolds number such that
after reaching it the flow regime in porous media
changes from a linear, Darcy's type law, to a nonlinear
and nonlocal law. We prove uniqueness for the
homogenized problem. The proof of convergence is given
under the usual assumption of periodic geometry",
ams = "35B27, 35Q30, 76a05, 76d05, 76s05",
keywords = "homogenization, nonlinear Darcy type law with memory,
2-scale convergence, periodic porous media,
quasi-Newtonian flow",
}
@InCollection{Brahim-Otsmane:1989:HT,
author = "S. Brahim-Otsmane and G. A. Francfort and F. Murat",
editor = "R. V. Kohn and G. W. Milton",
booktitle = "Random media and composites (Leesburg, VA, 1988)",
title = "Homogenization in thermoelasticity",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "13--45",
year = "1989",
}
@Article{Brahim-Otsmane:1992:CHW,
author = "S. Brahim-Otsmane and G. A. Francfort and F. Murat",
title = "Correctors for the homogenization of the wave and heat
equations",
journal = j-J-MATH-PURES-APPL,
volume = "71",
number = "3",
pages = "197--231",
year = "1992",
CODEN = "JMPAAM",
ISSN = "0021-7824",
fjournal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es.
Neuvi{\'e}me S{\'e}rie",
}
@Booklet{Braides:19xx:SCH,
author = "A. Braides",
title = "Semicontinuity, ${\Gamma }$-convergence and
Homogenization of Multiple Integrals",
year = "19xx",
abstract = "The paper contains the lecture notes of a 36-hour
course (18 lessons) held at SISSA, Trieste in 1994 on
the homogenization of (periodic/almost periodic)
nonlinear functionals (depending on vector-valued
functions) by Gamma-convergence techniques.",
}
@Article{Bratus:1983:BSEa,
author = "A. S. Bratus{\cprime} and A. P. Seyranian",
title = "Bimodal Solutions in Eigenvalue Optimization
Problems",
journal = j-PRIKL-MAT-MEH,
volume = "47",
number = "",
pages = "451--457",
year = "1983",
CODEN = "AMMEEQ",
ISSN = "0253-4827",
}
@Article{Bratus:1983:BSEb,
author = "A. S. Bratus{\cprime} and A. P. Seiranian",
title = "Bimodal solutions in eigenvalue optimization
problems",
journal = j-PRIKL-MAT-MEH,
volume = "47",
number = "4",
pages = "546--554",
year = "1983",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR87h:49049",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Bratus:1983:DEO,
author = "A. S. Bratus{\cprime} and A. P. Se{\u\i}ranyan",
title = "Double eigenvalues in optimization problems",
journal = j-DOKL-AKAD-NAUK,
volume = "272",
number = "2",
pages = "275--278",
year = "1983",
CODEN = "DANKAS",
ISSN = "0002-3264",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Bratus:1985:SCE,
author = "A. S. Bratus{\cprime}",
title = "The sufficient conditions for an extremum in problems
of optimizing the shapes of elastic plates",
journal = j-PRIKL-MAT-MEH,
volume = "49",
number = "4",
pages = "608--615",
year = "1985",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR87j:73089",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Bratus:1986:MEP,
author = "A. S. Bratus{\cprime}",
title = "Multiple eigenvalues in problems of optimization of
spectral properties of systems with a finite number of
degrees of freedom",
journal = j-Z-VYCISL-MAT-MAT-FIZ,
volume = "26",
number = "5",
pages = "645--654, 797",
year = "1986",
CODEN = "ZVMFAN",
ISSN = "0044-4669",
MRnumber = "MR87j:73090",
fjournal = "Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime
no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki",
}
@Article{Bratus:1989:EEP,
author = "A. S. Bratus{\cprime} and A. D. Myshkis",
title = "Extremal eigenvalue problems with a free boundary for
the {Laplace} operator and their applications",
journal = j-DIN-SPLOS-SREDY,
number = "91",
pages = "3--20, 168",
year = "1989",
CODEN = "DSSYAH",
ISSN = "0420-0497",
MRnumber = "MR92c:35084",
fjournal = "Institut Gidrodinamiki Sibirskogo Otdeleniya Akademii
Nauk SSSR. Dinamika Sploshno\u\i\ Sredy",
}
@Article{Bratus:1992:RBF,
author = "A. S. Bratus{\cprime} and A. D. Myshkis",
title = "On the ratio between the first and the second
eigenfrequency of the oscillations of a membrane",
journal = j-Z-VYCISL-MAT-MAT-FIZ,
volume = "32",
number = "2",
pages = "320--325",
year = "1992",
CODEN = "ZVMFAN",
ISSN = "0044-4669",
MRnumber = "MR93b:35030",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Zhurnal
Vychislitel\cprime no\u\i \ Matematiki i
Matematichesko\u\i\ Fiziki",
}
@Article{Bratus:1993:VCI,
author = "A. S. Bratus",
title = "On various cases of instability for elastic
nonconservative systems with damping",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "30",
number = "24",
pages = "3431--3441",
year = "1993",
CODEN = "IJSOAD",
ISSN = "0020-7683",
MRnumber = "MR95e:73028",
fjournal = "International Journal of Solids and Structures",
}
@Article{Bratus:1994:PSC,
author = "A. S. Bratus{\cprime}",
title = "On the properties of solutions of a class of
isoperimetric problems of stability optimization",
journal = j-PRIKL-MAT-MEH,
volume = "58",
number = "6",
pages = "86--95",
year = "1994",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR96a:34051",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Prikladnaya Matematika
i Mekhanika",
}
@Book{Brocker:1985:RCL,
author = "T. Br{\"{o}}cker and T. tom Dieck",
title = "Representations of Compact Lie groups",
volume = "98",
publisher = pub-SV,
address = pub-SV:adr,
year = "1985",
series = "Graduate Texts in Mathematics",
}
@Book{Brons:1997:PIM,
editor = "M. Br{\o}ns and M. P. Bend\-s{\o}e and M. P.
S{\o}rensen",
fulleditor = "Morton Br{\o}ns and M. P. Bend\-s{\o}e and Mads Peter
S{\o}rensen",
title = "Progress in industrial mathematics at {ECMI} 96",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "449",
year = "1997",
ISBN = "3-519-02607-4",
note = "Papers from the 9th European Conference for
Mathematics in Industry held at the Technical
University of Denmark, Lyngby, June 1996.",
}
@PhdThesis{Bruggeman:1930:EK,
author = "D. A. G. Bruggemann",
title = "{Elastizit{\"a}tskonstanten von Kristallaggregaten}",
school = "Universiteit te Verdedigen",
address = "Den Haag",
year = "1930",
}
@Article{Bruggemann:1935:BVP,
author = "D. A. G. Bruggemann",
title = "{Berechnung verschiedener physikalischer Konstanten
von heterogenen Substanzen. {I}.
Dielectrizit{\'a}tkonstanten und Leitf{\"a}higkeiten
der Mischk{\"o}rper aus isotropen Substanzen}",
journal = j-ANN-PHYS-1900,
volume = "22",
pages = "636--679",
year = "1935",
}
@Article{Bruggemann:1937:BVP,
author = "D. A. G. Bruggemann",
title = "{Berechnung verschiedener physikalischer Konstanten
von heterogenen Substanzen. {III}. Die elastische
Konstanten der Quasiisotropen Mischk{\"o}rper aus
isotropen Substanzen}",
journal = j-ANN-PHYS-1900,
volume = "29",
pages = "160--178",
year = "1937",
}
@Article{Bruno:1990:ECI,
author = "O. P. Bruno",
title = "The effective conductivity of an infinitely
interchangeable mixture",
journal = j-COMM-PURE-APPL-MATH,
volume = "43",
number = "6",
pages = "769--807",
year = "1990",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
MRnumber = "MR91i:73003",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Bruno:1990:IBE,
author = "O. P. Bruno and K. Golden",
title = "Interchangeability and bounds on the effective
conductivity of the square lattice",
journal = j-J-STAT-PHYS,
volume = "61",
number = "1-2",
pages = "365--386",
year = "1990",
CODEN = "JSTPSB",
ISSN = "0022-4715",
fjournal = "Journal of Statistical Physics",
}
@InCollection{Bruno:1991:ECC,
author = "O. P. Bruno",
booktitle = "Mathematics of random media (Blacksburg, VA, 1989)",
title = "The effective conductivity of composites",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "293--300",
year = "1991",
MRnumber = "MR92k:82074",
}
@Article{Bruno:1991:ECS,
author = "O. P. Bruno",
title = "The effective conductivity of strongly heterogeneous
composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "433",
number = "1888",
pages = "353--381",
year = "1991",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
MRnumber = "MR92c:82111",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Bruno:1991:TEB,
author = "O. P. Bruno",
title = "Taylor expansions and bounds for the effective
conductivity and the effective elastic moduli of
multicomponent composites and polycrystals",
journal = j-ASYMPTOT-ANAL,
volume = "4",
number = "4",
pages = "339--365",
year = "1991",
CODEN = "ASANEZ",
ISSN = "0921-7134",
MRnumber = "MR93c:73072",
fjournal = "Asymptotic Analysis",
}
@Article{Bruno:1992:SBV,
author = "O. P. Bruno and F. Reitich",
fullauthor = "O. P. Bruno and Fernando Reitich",
title = "Solution of a boundary value problem for the
{Helmholtz} equation via variation of the boundary into
the complex domain",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "122",
number = "3-4",
pages = "317--340",
year = "1992",
CODEN = "PEAMDU",
ISSN = "0308-2105",
MRnumber = "MR94e:35131",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Bruno:1992:SMC,
author = "O. P. Bruno and P. H. Leo",
title = "On the stiffness of materials containing a disordered
array of microscopic holes or hard inclusions",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "121",
number = "4",
pages = "303--338",
year = "1992",
CODEN = "AVRMAW",
ISSN = "0003-9527",
MRnumber = "MR93k:73005",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Bruno:1994:AAF,
author = "O. P. Bruno and F. Reitich",
title = "Approximation of analytic functions: a method of
enhanced convergence",
journal = j-MATH-COMPUT,
volume = "63",
number = "207",
pages = "195--213",
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718",
MRnumber = "MR94m:30003",
fjournal = "Mathematics of Computation",
}
@InCollection{Bruno:1997:EM,
author = "O. P. Bruno",
booktitle = "Smart structures and materials 1997: mathematics and
control in smart structures (San Diego, CA)",
title = "Energetics in martensites",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "14--24",
year = "1997",
MRnumber = "MR1475733",
}
@InCollection{Bruno:1998:BEE,
author = "O. P. Bruno and F. Reitich",
booktitle = "Mathematics of multiscale materials (Minneapolis, MN,
1995--1996)",
title = "Bounds on the effective elastic properties of
martensitic polycrystals",
publisher = pub-SV,
address = "New York",
pages = "51--62",
year = "1998",
MRnumber = "MR1636011",
}
@InCollection{Bruno:1998:FHO,
author = "O. P. Bruno and A. Sei",
booktitle = "Mathematical and numerical aspects of wave propagation
(Golden, CO, 1998)",
title = "A fast high-order solver for problems of scattering by
heterogeneous bodies",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "270--274",
year = "1998",
MRnumber = "MR1635337",
}
@InProceedings{Budiansky:1960:SFS,
author = "B. Budiansky and Z. Hashin and J. Lyell {Sanders,
Jr.}",
booktitle = "Plasticity: Proceedings of the Second Symposium on
Naval Structural Mechanics",
title = "The stress field of a slipped crystal and the early
plastic behavior of polycrystalline materials",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "239--258",
year = "1960",
MRnumber = "MR26:953",
}
@Book{Buikis:1983:CPZ,
editor = "A. A. Bu{\u\i}kis",
title = "{\cyr {Prikladnye} zadachi matematichesko\u\i\
fiziki}",
publisher = "Latv. Gos. Univ.",
address = "Riga",
pages = "175",
year = "1983",
}
@Article{Burns:1997:ODM,
author = "T. Burns and A. V. Cherkaev",
title = "Optimal distribution of multimaterial composites for
torsional beams",
journal = j-STRUCT-OPTIM,
volume = "13",
number = "1",
pages = "14--23",
year = "1997",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
searchkey = "au:cherkaev, a",
}
@Article{Butkovsky:1968:OCD,
author = "A. G. Butkovsky and A. I. Egorov and K. A. Lurie",
title = "Optimal control of distributed systems (a survey of
{Soviet} publications)",
journal = j-SIAM-J-CONTROL,
volume = "6",
pages = "437--476",
year = "1968",
CODEN = "SJCOA9",
ISSN = "0036-1402",
}
@Book{Buttazzo:1989:SRI,
author = "G. Buttazzo",
title = "Semicontinuity, relaxation and integral representation
in the calculus of variations",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "iv + 222",
year = "1989",
ISBN = "0-582-01859-5",
}
@Article{Buttazzo:19xx:EVM,
author = "G. Buttazzo",
title = "Energies on ${BV}$ and Variational Models in Fracture
Mechanics",
year = "19xx",
abstract = "In the paper we consider variational models for
problems arising from fracture mechanics; more
precisely the space of admissible states
(displacements) is taken as the space $BV$ of functions
with bounded variation and the fracture is the set
where the displacement is discontinuous. A discussion
on the lower semicontinuity of the stored energy
functional is made, together with the associated
relaxation results",
}
@Article{Buttazzo:19xx:GTR,
author = "G. Buttazzo",
title = "A general theory of relaxed controls and application
to shape optimization problems",
journal = "Proceedings of ``PDE of Elliptic Type'', Capri 1994,
Pitman Res. Notes Math. Series",
volume = "??",
number = "??",
pages = "??--??",
year = "19xx",
abstract = "We present a general formulation for relaxed optimal
control problems. In the case of shape optimization
problems governed by an elliptic equation with
Dirichlet condition on the free interface we show an
existence result for relaxed solutions and, under a
monotonicity assumption on the cost, an existence
result for classic solutions. Several examples are
given.",
ams = "49J45, 35J25, 49R05",
keywords = "Relaxed controls, Shape optimization, Eigenvalues
optimization",
}
@Book{Callen:1960:T,
author = "H. B. Callen",
title = "Thermodynamics",
publisher = "John Wiley \& Sons, Inc.",
address = "New York",
year = "1960",
}
@Book{Caratheodory:1965:CVP,
author = "C. Carath{\'e}odory",
title = "Calculus of variations and partial differential
equations of the first order. {Part I}: {Partial}
differential equations of the first order",
publisher = "Holden-Day Inc.",
address = "San Francisco",
pages = "xvi + 171",
year = "1965",
note = "Translated by Robert B. Dean and Julius J.
Brandstatter.",
}
@Book{Caratheodory:1967:CVP,
author = "C. Carath{\'e}odory",
title = "Calculus of variations and partial differential
equations of the first order. {Part II}: {Calculus} of
variations",
publisher = "Holden-Day Inc.",
address = "San Francisco, Calif.",
pages = "xvi + 175--398",
year = "1967",
note = "Translated from the German by Robert B. Dean, Julius
J. Brandstatter, translating editor.",
}
@Book{Caratheodory:1994:VPD,
author = "C. Carath{\'e}odory",
title = "Variationsrechnung und partielle
{Differentialgleichungen} erster {Ordnung}",
publisher = "B. G. Teubner Verlagsgesellschaft mbH",
address = "Stuttgart",
pages = "365",
year = "1994",
ISBN = "3-8154-2019-9",
note = "Variationsrechnung. [Calculus of variations], With
contributions by H. Boerner and E. H{\"o}lder, Edited
and with comments and supplements by R. Kl{\"o}tzler",
}
@Article{Carmona:1997:HTD,
author = "R. A. Carmona and Lin Xu",
fullauthor = "Ren{\'e} A. Carmona and Lin Xu",
title = "Homogenization for time-dependent two-dimensional
incompressible {Gaussian} flows",
journal = j-ANN-APPL-PROBAB,
volume = "7",
number = "1",
pages = "265--279",
year = "1997",
ISSN = "1050-5164",
fjournal = "The Annals of Applied Probability",
}
@Article{Carothers:1912:PSW,
author = "S. D. Carothers",
title = "Plane strain in a wedge",
journal = j-PROC-R-SOC-EDINB,
volume = "23",
number = "",
pages = "292",
year = "1912",
CODEN = "PRSEAE",
ISSN = "0080-4541",
}
@Article{Castaneda:1988:OPN,
author = "P. {Ponte Cast\-a\-{\~n}e\-da} and J. R. Willis",
title = "On the overall properties of nonlinearly viscous
composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "416",
number = "1850",
pages = "217--244",
year = "1988",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Castaneda:1992:BEP,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
title = "Bounds and estimates for the properties of nonlinear
heterogeneous systems",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "340",
number = "1659",
pages = "531--567",
year = "1992",
CODEN = "PTMSFB",
ISSN = "0962-8428",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Physical Sciences and Engineering",
}
@Article{Castaneda:1992:NVPa,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
title = "A new variational principle and its application to
nonlinear heterogeneous systems",
journal = j-SIAM-J-APPL-MATH,
volume = "52",
number = "5",
pages = "1321--1341",
year = "1992",
CODEN = "SMJMAP",
ISSN = "0036-1399",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Castaneda:1992:NVPb,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
title = "New variational principles in plasticity and their
application to composite materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "40",
number = "8",
pages = "1757--1788",
year = "1992",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Castaneda:1995:EMB,
author = "P. {Ponte Cast\-a\-{\~n}e\-da} and P. Suquet",
title = "On the effective mechanical behavior of weakly
inhomogeneous nonlinear materials",
journal = j-EUR-J-MECH-A-SOLIDS,
volume = "14",
number = "2",
pages = "205--236",
year = "1995",
CODEN = "EJASEV",
ISSN = "0997-7538",
fjournal = "European Journal of Mechanics. A Solids",
}
@Article{Castaneda:1996:ESO,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
title = "Exact second-order estimates for the effective
mechanical properties of nonlinear composite
materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "44",
number = "6",
pages = "827--862",
year = "1996",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Castaneda:1996:SNC,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
title = "Strongly nonlinear composites: a second-order theory
for estimating transport properties",
journal = j-PHYS-LET-A,
volume = "224",
number = "3",
pages = "163--168",
year = "1996",
CODEN = "PYLAAG",
ISSN = "0375-9601",
fjournal = "Physics Letters. A",
}
@Article{Castaneda:1997:ENE,
author = "P. {Ponte Cast\-a\-{\~n}e\-da} and M. Kailasam",
title = "Errata: ``{Nonlinear} electrical conductivity in
heterogeneous media''",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "453",
number = "",
pages = "1791",
year = "1997",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@InCollection{Castaneda:1997:NCM,
author = "P. {Ponte Cast\-a\-{\~n}e\-da}",
booktitle = "Continuum micromechanics",
title = "Nonlinear composite materials: effective constitutive
behavior and microstructure evolution",
publisher = pub-SV,
address = "Vienna",
pages = "131--195",
year = "1997",
}
@Article{Castaneda:1997:NEC,
author = "P. {Ponte Cast\-a\-{\~n}e\-da} and M. Kailasam",
title = "Nonlinear electrical conductivity in heterogeneous
media",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "453",
number = "1959",
pages = "793--816",
year = "1997",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Castaneda:1997:VES,
author = "P. {Ponte Cast\-a\-{\~n}e\-da} and M. V. Nebozhyn",
title = "Variational estimates of the self-consistent type for
the effective behaviour of some model nonlinear
polycrystals",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "453",
number = "1967",
pages = "2715--2724",
year = "1997",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Charalambakis:1989:WSI,
author = "N. Charalambakis and F. Murat",
fullauthor = "Nicolas Charalambakis and F. Murat",
title = "Weak solutions to the initial-boundary value problem
for the shearing of nonhomogeneous thermoviscoplastic
materials",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "113",
number = "3-4",
pages = "257--265",
year = "1989",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Cheng:1981:ICO,
author = "G. Cheng and N. Olhoff",
title = "An Investigation Concerning Optimal Design of Solid
Elastic Plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "17",
number = "",
pages = "305--323",
year = "1981",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Cheng:1982:RFO,
author = "G. Cheng and N. Olhoff",
title = "Regularized Formulation for Optimal Design of
Axisymmetric Plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "18",
number = "2",
pages = "153--169",
year = "1982",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Cherepanov:1974:IPP,
author = "G. P. Cherepanov",
title = "Inverse problems of the plane theory of elasticity",
journal = j-J-APPL-MATH-MECH,
volume = "38",
number = "6",
pages = "963--979",
year = "1974",
CODEN = "JAMMAR",
ISSN = "0021-8928",
}
@InCollection{Cherkaev:1987:I,
author = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "Introduction",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "273--317",
year = "1987",
}
@Article{Cherkaev:1988:ODN,
author = "A. V. Cherkaev and L. V. Gibiansky",
title = "Optimal design of nonlinear-elastic and
elastic-plastic torsioned bars",
journal = j-MECH-SOLIDS,
volume = "5",
pages = "168--174",
year = "1988",
CODEN = "MESOBN",
ISSN = "0025-6544",
}
@Article{Cherkaev:1992:ECB,
author = "A. V. Cherkaev and L. V. Gibiansky",
title = "The exact coupled bounds for effective tensors of
electrical and magnetic properties of two-component
two-dimensional composites",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "122",
number = "1-2",
pages = "93--125",
year = "1992",
CODEN = "PEAMDU",
ISSN = "0308-2105",
MRclass = "73B27 (73K20 73R05 73V25 78A30)",
MRnumber = "93k:73006",
MRreviewer = "Serguei M. Kozlov",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "First version \cite{Gibiansky:1988:DCP} (in Russian)",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Cherkaev:1992:IPS,
author = "A. V. Cherkaev and K. A. Lurie and G. W. Milton",
title = "Invariant properties of the stress in plane elasticity
and equivalence classes of composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "438",
number = "1904",
pages = "519--529",
month = sep,
year = "1992",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
MRclass = "73B27 (73C99 73K20)",
MRnumber = "93g:73009",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
searchkey = "au:cherkaev, a",
xxtitle = "Invariant properties of stress in plane elasticity and
equivalence classes of composites",
}
@Article{Cherkaev:1993:CEB,
author = "A. V. Cherkaev and L. V. Gibiansky",
title = "Coupled estimates for the bulk and shear moduli of a
two-dimensional isotropic elastic composite",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "41",
number = "5",
pages = "937--980",
month = may,
year = "1993",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRclass = "73B27 (73K20)",
MRnumber = "94e:73002",
MRreviewer = "J. Saint Jean Paulin",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Mechanics and Physics of Solids",
searchkey = "au:cherkaev, a",
}
@InProceedings{Cherkaev:1993:SOS,
author = "A. V. Cherkaev",
booktitle = "Topology design of structures (Sesimbra, 1992),",
title = "Stability of optimal structures of elastic
composites",
volume = "227",
publisher = pub-KLUWER,
address = "Dordrecht",
pages = "547--558",
year = "1993",
MRclass = "73K20 (73K40)",
MRnumber = "1 250 207",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
series = "{NATO} Adv. Sci. Inst. Ser. {E} Appl. Sci.",
acknowledgement = ack-nhfb,
}
@Article{Cherkaev:1994:RPO,
author = "A. V. Cherkaev",
title = "Relaxation of problems of optimal structural design",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "31",
number = "16",
pages = "2251--2280",
year = "1994",
CODEN = "IJSOAD",
ISSN = "0020-7683",
MRclass = "73K40 (49Q10 73B27 73K20 73V25)",
MRnumber = "95k:73068",
MRreviewer = "R. Lipton",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Solids and Structures",
}
@Article{Cherkaev:1994:VPC,
author = "A. V. Cherkaev and L. V. Gibiansky",
title = "Variational principles for complex conductivity,
viscoelasticity, and similar problems in media with
complex moduli",
journal = j-J-MATH-PHYS,
volume = "35",
number = "1",
pages = "127--145",
month = jan,
year = "1994",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
MRclass = "73V25 (35B27 73B27 73F15 73K20)",
MRnumber = "94k:73081",
MRreviewer = "Alexander Belyaev",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
searchkey = "au:cherkaev, a",
}
@InCollection{Cherkaev:1995:ROD,
author = "A. V. Cherkaev",
booktitle = "Proceedings of the Second Workshop on Composite Media
and Homogenization Theory (ICTP, Trieste, 1993)",
title = "Reducing of optimal design problems to minimal
variational problems",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "139--165",
year = "1995",
}
@Article{Cherkaev:1995:WES,
author = "A. V. Cherkaev and L. Slepyan",
title = "Waiting element structures and stability under
extension",
journal = j-INT-J-DAMAGE-MECH,
volume = "4",
pages = "58--82",
month = jan,
year = "1995",
CODEN = "IDMEEH",
}
@Article{Cherkaev:1996:ESM,
author = "A. V. Cherkaev and L. V. Gibiansky",
title = "Extremal structures of multiphase heat conducting
composites",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "33",
number = "18",
pages = "2609--2618",
year = "1996",
CODEN = "IJSOAD",
ISSN = "0020-7683",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
searchkey = "au:cherkaev, a",
}
@Article{Cherkaev:1996:ODT,
author = "A. V. Cherkaev and R. Palais",
title = "Optimal design of three-dimensional axisymmetric
structures",
journal = j-STRUCT-OPTIM,
volume = "13",
number = "1",
pages = "10--23",
month = "????",
year = "1997",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
searchkey = "au:cherkaev, a",
}
@Article{Cherkaev:1997:NIW,
author = "A. V. Cherkaev and R. Palais",
title = "{NIST-CTCMS} International Workshop on Optimal Design
for Materials and Structures",
journal = j-STRUCT-OPTIM,
volume = "13",
number = "1",
pages = "1--4",
month = "????",
year = "1997",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
acknowledgement = ack-nhfb,
searchkey = "au:cherkaev, a",
}
@Book{Cherkaev:1997:TMM,
editor = "A. V. Cherkaev and R. V. Kohn",
title = "Topics in the mathematical modelling of composite
materials",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xiv + 317",
year = "1997",
ISBN = "0-8176-3662-5",
}
@Article{Cherkaev:1998:COS,
author = "A. V. Cherkaev and Y. Grabovsky and A. B. Movchan and
S. K. Serkov",
title = "The cavity of the optimal shape under the shear
stresses",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "35",
number = "33",
pages = "4391--4410",
year = "1998",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@InProceedings{Cherkaev:1998:ODC,
author = "A. V. Cherkaev and Y. Grabovsky and A. B. Movchan and
S. K. Serkov",
booktitle = "Proceedings of IUTAM Symposium on Transformation
Problems in Composite and Active Materials",
title = "Optimality of dilute composites under shear load",
address = "",
pages = "00--00",
year = "1998",
note = "In print.",
}
@InCollection{Cherkaev:1998:ODT,
author = "A. V. Cherkaev and R. Palais",
editor = "C. T. Leondes",
booktitle = "Structural Dynamical Systems: Computational
Technologies and Optimization",
title = "Optimal design of Three-dimensional Axisymmetric
Elastic structures",
publisher = "Gordon and Breach Science Publ.",
pages = "237--267",
year = "1998",
}
@Article{Cherkaev:1998:SOD,
author = "A. V. Cherkaev and L. Krog and I. Kucuk",
title = "Stable optimal design of two-component elastic
structures",
journal = j-CONTROL-CYBERN,
volume = "27",
number = "2",
pages = "265--282",
year = "1998",
CODEN = "CCYBAP",
ISSN = "0324-8569",
}
@InCollection{Cherkaev:1998:VAS,
author = "A. V. Cherkaev",
editor = "C. T. Leondes",
booktitle = "Structural Dynamical Systems: Computational
Technologies and Optimization",
title = "Variational Approach to structural optimization",
publisher = "Gordon and Breach Science Publ.",
pages = "199--237",
year = "1998",
}
@Unpublished{Cherkaev:1999:NCP,
author = "A. V. Cherkaev and M. Miettinen",
title = "Necessary condition in the polycrystal ${G}$-closure
problem",
year = "1999",
note = "in preparation",
}
@Article{Cherkaev:1999:NCT,
author = "A. V. Cherkaev",
title = "Necessary conditions technique in structural
optimization",
journal = j-INT-J-SOLIDS-STRUCT,
year = "1999",
CODEN = "IJSOAD",
ISSN = "0020-7683",
note = "To appear.",
}
@InCollection{Cherkaev:1999:OHC,
author = "A. V. Cherkaev and T. C. Robbins",
booktitle = "Proceedings of the 3rd World Congress of Structural
and Multidisciplinary Optimization",
title = "Optimization of heat conducting structures",
publisher = "ISSMO",
address = "Buffalo, New York",
pages = "89",
year = "1999",
}
@Book{Cherkaev:1999:VMS,
author = "A. V. Cherkaev",
title = "Variational methods for structural optimization",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 618",
year = "1999",
note = "in print",
}
@InCollection{Cherkaeva:1995:BDM,
author = "E. Cherkaeva and A. V. Cherkaev",
booktitle = "Structural and multidisciplinary optimization",
title = "Bounds for detectability of material damage by noisy
electrical measurements",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "543--548",
year = "1995",
}
@Article{Cherkaeva:1996:ICP,
author = "E. Cherkaeva and A. C. Tripp",
title = "Inverse conductivity problem for inaccurate
measurements",
journal = j-INVERSE-PROBLEMS,
volume = "12",
number = "6",
pages = "869--883",
year = "1996",
CODEN = "INPEEY",
ISSN = "0266-5611",
fjournal = "Inverse Problems. An International Journal on the
Theory and Practice of Inverse Problems, Inverse
Methods and Computerized Inversion of Data",
}
@Article{Cherkaeva:1997:OSC,
author = "E. Cherkaeva",
title = "Optimal source control and resolution in
nondestructive testing",
journal = j-STRUCT-OPTIM,
volume = "13",
number = "1",
pages = "12--16",
year = "1997",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
xxjournal = "Int. J. Structural Optimization",
}
@InCollection{Cherkaeva:1997:SOI,
author = "E. Cherkaeva and A. C. Tripp",
booktitle = "Inverse problems in geophysical applications
(Yosemite, CA, 1995)",
title = "Source optimization in the inverse geoelectrical
problem",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "240--256",
year = "1997",
}
@InCollection{Cherkaeva:1998:ODU,
author = "E. Cherkaeva and A. V. Cherkaev",
booktitle = "Homogenization",
title = "Optimal design for uncertain loading conditions",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "in print",
year = "1998",
}
@InCollection{Cherkaeva:1998:SOB,
author = "E. Cherkaeva and A. V. Cherkaev",
editor = "P. Pedersen and M. Bend\-s{\o}e",
booktitle = "Synthesis in bio solid mechanics",
title = "Structural optimization and biological {"designs"}
",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "247--264",
year = "1999",
series = "Solid mechanics and its applications",
}
@Article{Chiheb:1998:OFR,
author = "R. Chiheb and G. P. Panasenko",
title = "Optimization of finite rod structures and
{L}-convergence",
journal = j-J-DYN-CONTROL-SYST,
volume = "4",
number = "2",
pages = "273--304",
year = "1998",
CODEN = "JDCSEK",
ISSN = "1079-2724",
fjournal = "Journal of Dynamical and Control Systems",
}
@Book{Christensen:1971:TV,
author = "R. M. Christensen",
title = "Theory of Viscoelasticity",
publisher = pub-AP,
address = pub-AP:adr,
year = "1971",
}
@Book{Christensen:1979:MCM,
author = "R. M. Christensen",
title = "Mechanics of Composite Materials",
publisher = pub-WI,
address = pub-WI:adr,
year = "1979",
}
@Book{Chui:1997:WMT,
author = "Charles K. Chui",
title = "Wavelets: a mathematical tool for signal processing",
publisher = "Society for Industrial and Applied Mathematics
(SIAM)",
address = "Philadelphia, PA",
pages = "xviii + 210",
year = "1997",
ISBN = "0-89871-384-6",
MRnumber = "MR1443204",
note = "With a foreword by G. Strang.",
}
@Article{Cioranescu:1982:TEV,
author = "D. Cioranescu and F. Murat",
booktitle = "Nonlinear partial differential equations and their
applications. Coll\`ege de France Seminar, Vol. III
(Paris, 1980/1981)",
title = "Un terme \'etrange venu d'ailleurs. {II}",
publisher = "Pitman",
address = "Boston, Mass.",
pages = "154--178, 425--426",
year = "1982",
note = "Translated to English in \cite{Cioranescu:1997:STC}",
abstract = "Let $\Omega$ be an open bounded set of $R^N (N \ge
2)$, for each $\epsilon > 0$, we make some holes in
$\Omega$, and obtain an open set $\Omega^\varepsilon$.
Let $u^\varepsilon$ be the solution of the {Dirichlet}
problem in $\Omega^\varepsilon$ (for fixed right
number): ?? hier fehlt equation0 Our problem is to
determine if the $u^\varepsilon$ has a limit, if
possible, what is the equation satisfied by this limit.
We are interested in non-classical cases, and we
exclude the cases where the characteristic function of
the holes goes to a strictly positive function, or
where the compact sets of $\Omega$ are absorbed by the
$\Omega^\varepsilon$. The typical case we consider is
the following: we cover $R^N$ with cubes of size
$\varepsilon$; in the middle of each we make a hole of
size $\varepsilon^{N/(N-2)}$ (if $N \ge 3$) or $\exp (-
\frac{1}{2})$ (if $N=2$). Then $\tilde{u^\varepsilon}$
goes weakly to $u$ in $H{{_0}{^1}}(\Omega)$, where $u$
is the solution of: (?? hier fehlt equation1). Here
$\mu$ is a constant: $\mu \in R, \mu > 0$. The work is
divided in four parts: in the first, we introduce an
abstract framework in order to pass to the limit in
(1): the idea is to suppose the existence of good test
functions $w^\varepsilon$, as in the energy method in
the theory of homogenization; we obtain an equation of
type (2), with $\mu \in H^{-1}(\Omega), \mu \ge 0$. The
method can be extended to {Dirichlet} problems of any
order. In the second part, we give examples. In the
third part, we prove (in the abstract framework) the
lower semi-continuity of the energy and the following
result: the solution $u^\varepsilon$ of (1) (apart from
a remainder which goes strongly to zero) is the product
of the test function $w^\varepsilon$ by the limit
function $u$, which is the solution of (2). The fourth
part is devoted to the study of variational
inequalities of obstacle type, related to the above
{Dirichlet} problems in the following way: for a given
function $\psi$, we define the obstacles
$\psi^\varepsilon$ by: ?? hier fehlt array",
}
@Article{Cioranescu:1991:HCW,
author = "D. Cioranescu and P. Donato and F. Murat and E.
Zuazua",
title = "Homogenization and corrector for the wave equation in
domains with small holes",
journal = j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
volume = "18",
number = "2",
pages = "251--293",
year = "1991",
CODEN = "PSNAAI",
ISSN = "0391-173X",
fjournal = "Annali della Scuola Normale Superiore di Pisa. Classe
di Scienze. Serie IV",
}
@Article{Cioranescu:1992:FFD,
author = "D. Cioranescu and P. Donato and H. I. Ene",
title = "Fluid Flows in Dielectric Porous Media",
journal = j-INT-SER-NUMER-MATH,
volume = "107",
pages = "3--10",
year = "1992",
ISSN = "0539-0141",
}
@Article{Cioranescu:1997:STC,
author = "D. Cioranescu and F. Murat",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modeling of composite
materials",
title = "A strange term coming from nowhere",
volume = "31",
publisher = "Birkh{\"a}user",
address = "Boston",
pages = "45--93",
year = "1997",
note = "Translation of the paper \cite{Cioranescu:1982:TEV}",
series = "Progress in nonlinear differential equations and their
applications",
}
@TechReport{Cioranescu:19xx:NHN,
author = "D. Cioranescu",
title = "Non Homogeneous {Neumann} Problems in Perforated
Domains",
year = "19xx",
}
@Article{Clark:1994:MEC,
author = "K. E. Clark and G. W. Milton",
title = "Modelling the effective conductivity function of an
arbitrary two-dimensional polycrystal using sequential
laminates",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "124",
number = "4",
pages = "757--783",
year = "1994",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Clark:1995:OBC,
author = "K. E. Clark and G. W. Milton",
title = "Optimal bounds correlating electric, magnetic and
thermal properties of two-phase, two-dimensional
composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "448",
number = "1933",
pages = "161--190",
year = "1995",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Book{Clarke:1983:ONA,
author = "F. H. Clarke",
title = "Optimization and Nonsmooth Analysis",
publisher = "John Wiley \& Sons, Inc.",
address = "New York",
year = "1983",
}
@Book{Clegg:1968:CV,
author = "J. C. Clegg",
title = "Calculus of variations",
publisher = "Oliver \& Boyd",
address = "Edinburgh",
pages = "ix + 190",
year = "1968",
note = "University Mathematical Texts, No. 38.",
}
@Book{Clemens:1978:SOC,
author = "D. J. Clements and B. D. O. Anderson",
title = "Singular optimal control: the linear-quadratic
problem",
publisher = pub-SV,
address = "Berlin",
pages = "v + 93",
year = "1978",
note = "Lecture Notes in Control and Information Sciences,
Vol. 5.",
}
@Article{Clerc:1990:ECB,
author = "J. P. Clerc and G. Giraud and J. Laugier and J. Luck",
title = "The electrical conductivity of binary disordered
systems, percolation clusters, fractals and related
models",
journal = j-ADV-PHYS,
volume = "39",
pages = "191--309",
year = "1990",
CODEN = "ADPHAH",
ISSN = "0001-8732",
}
@Article{Collins:1991:NAS,
author = "C. Collins and D. Kinderlehrer and M. Luskin",
title = "Numerical approximation of the solution of a
variational problem with a double well potential",
journal = j-SIAM-J-NUMER-ANAL,
volume = "28",
number = "2",
pages = "321--332",
year = "1991",
CODEN = "SJNAAM",
ISSN = "0036-1429",
MRnumber = "MR92c:73015",
fjournal = "SIAM Journal on Numerical Analysis",
}
@InCollection{Collins:1993:CRT,
author = "C. Collins and M. Luskin and J. Riordan",
editor = "D. Kinderlehrer and R. James and M. Luskin and J. L.
Ericksen",
booktitle = "Microstructure and phase transition",
title = "Computational results for a two-dimensional model of
crystalline microstructure",
publisher = pub-SV,
address = "New York",
pages = "51--56",
year = "1993",
MRnumber = "MR95m:73020",
}
@Article{Conca:1994:SNS,
author = "C. Conca and F. Murat and O. Pironneau",
title = "The {Stokes} and {Navier-Stokes} equations with
boundary conditions involving the pressure",
journal = j-JAPAN-J-MATH-N-S,
volume = "20",
number = "2",
pages = "279--318",
year = "1994",
CODEN = "JJMAAK",
ISSN = "0289-2316",
fjournal = "Japanese Journal of Mathematics. New Series",
}
@Book{Cook:1989:CAF,
author = "R. D. Cook and D. S. Malkus and M. E. Plesha",
editor = "",
title = "Concepts and Applications of Finite Element Analysis",
volume = "",
publisher = "Wiley \& Sons",
address = "New York",
edition = "Third",
month = "",
year = "1989",
series = "",
}
@Book{Courant:1962:MMP,
author = "R. Courant and D. Hilbert",
title = "Methods of Mathematical Physics",
publisher = pub-INTERSCI,
address = pub-INTERSCI:adr,
pages = "",
year = "1962",
}
@Article{Cox:1992:ODC,
author = "S. J. Cox and M. L. Overton",
title = "On the optimal design of columns against buckling",
journal = j-SIAM-J-MATH-ANA,
volume = "23",
number = "2",
pages = "287--325",
year = "1992",
CODEN = "SJMAAH",
ISSN = "0036-1410",
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Cox:1996:EEP,
author = "S. Cox and R. Lipton",
title = "Extremal eigenvalue problems for two-phase
conductors",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "136",
number = "2",
pages = "101--117",
year = "1996",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Crandall:1979:RGA,
author = "M. G. Crandall and A. Pazy and L. Tartar",
title = "Remarks on generators of analytic semigroups",
journal = j-ISRAEL-J-MATH,
volume = "32",
number = "4",
pages = "363--374",
year = "1979",
CODEN = "ISJMAP",
ISSN = "0021-2172",
fjournal = "Israel Journal of Mathematics",
}
@Article{Crandall:1980:SRB,
author = "M. G. Crandall and L. Tartar",
title = "Some relations between nonexpansive and order
preserving mappings",
journal = j-PROC-AM-MATH-SOC,
volume = "78",
number = "3",
pages = "385--390",
year = "1980",
CODEN = "PAMYAR",
ISSN = "0002-9939",
fjournal = "Proceedings of the American Mathematical Society",
}
@Article{Cribb:1968:STE,
author = "J. L. Cribb",
title = "Shrinkage and thermal expansion of a two-phase
material",
journal = j-NATURE,
volume = "220",
pages = "576--577",
year = "1968",
CODEN = "NATUAS",
ISSN = "0028-0836",
}
@Book{Dacorogna:1982:WCW,
author = "B. Dacorogna",
title = "Weak continuity and weak lower semicontinuity of
nonlinear functionals",
publisher = pub-SV,
address = "Berlin",
pages = "iii + 120",
year = "1982",
ISBN = "3-540-11488-2",
}
@Book{Dacorogna:1989:DMC,
author = "B. Dacorogna",
title = "Direct methods in the calculus of variations",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 308",
year = "1989",
ISBN = "3-540-50491-5",
}
@Article{Dacorogna:1992:OCS,
author = "B. Dacorogna and F. Murat",
title = "On the optimality of certain {Sobolev} exponents for
the weak continuity of determinants",
journal = j-J-FUNCT-ANAL,
volume = "105",
number = "1",
pages = "42--62",
year = "1992",
CODEN = "JFUAAW",
ISSN = "0022-1236",
fjournal = "Journal of Functional Analysis",
}
@InCollection{Dacorogna:1996:RNS,
author = "B. Dacorogna and J.-P. Haeberly",
booktitle = "Variational methods for discontinuous structures
(Como, 1994)",
title = "Remarks on a numerical study of convexity,
quasiconvexity, and rank one convexity",
publisher = "Birkh{\"a}user",
address = "Basel",
pages = "143--154",
year = "1996",
}
@Article{DalMaso:19xx:LCC,
author = "G. DalMaso and R. V. Kohn",
title = "The local character of {$G$}-closure",
year = "19xx",
}
@Article{DellAntonio:1986:ATO,
author = "G. F. Dell'Antonio and R. Figari and E. Orlandi",
title = "An approach through orthogonal projections to the
study of inhomogeneous random media with linear
response",
journal = j-ANN-INST-HENRI-POINCARE-B,
volume = "44",
pages = "1--28",
year = "1986",
CODEN = "AHPBAR",
ISSN = "0020-2347",
}
@Article{DellAntonio:1988:GRE,
author = "G. F. Dell'Antonio and V. Nesi",
title = "A general representation for the effective dielectric
constant of a composite",
journal = j-J-MATH-PHYS,
volume = "29",
number = "12",
pages = "2688--2694",
year = "1988",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
fjournal = "Journal of Mathematical Physics",
}
@Article{DellAntonio:1990:SIW,
author = "G. F. Dell'Antonio and V. Nesi",
title = "A scalar inequality which bounds the effective
conductivity of composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "431",
number = "1883",
pages = "519--530",
year = "1990",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Book{Demprimeyanov:1990:IM,
author = "V. F. Dem{\cprime}yanov and V. N. Maloz{\"e}mov",
title = "Introduction to minimax",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "viii + 307",
year = "1990",
ISBN = "0-486-66423-6",
note = "Translated from the Russian by D. Louvish, Reprint of
the 1974 edition.",
}
@Article{Diaz:1992:SOS,
author = "A. R. D{\'\i}az and M. P. Bend\-s{\o}e",
title = "Shape Optimization of Structures for Multiple Loading
Situations using a Homogenization Method",
journal = j-STRUCT-OPTIM,
volume = "4",
number = "",
pages = "17--22",
year = "1992",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
xxtitle = "Shape optimization of structures for multiple loading
conditions using a homogenization method",
}
@Article{Diaz:1992:SST,
author = "A. R. D{\'\i}az and N. Kikuchi",
title = "Solution to Shape and Topology Eigenvalue Optimization
Problems using a Homogenization Method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "35",
number = "",
pages = "1487--1502",
year = "1992",
CODEN = "IJNMBH",
ISSN = "0029-5981",
}
@Article{Diaz:1993:DOG,
author = "A. R. D{\'\i}az and N. Kikuchi and P. Y. Papalambros
and J. E. Taylor",
title = "Design of an optimal grid for finite element methods",
journal = j-J-STRUCT-MECH,
volume = "11",
number = "2",
pages = "215--230",
year = "1993",
CODEN = "JSMHA2",
ISSN = "0360-1218",
fjournal = "Journal of Structural Mechanics",
}
@Article{Diaz:1994:NFP,
author = "A. R. D{\'\i}az and R. Lipton and C. A. Soto",
title = "A New Formulation of the Problem of Optimum
Reinforcement of {Reissner-Mindlin} Plates",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "",
number = "",
pages = "",
year = "1994",
CODEN = "CMMECC",
ISSN = "0045-7825",
}
@Article{Diaz:1995:CPL,
author = "A. R. D{\'\i}az and O. Sigmund",
title = "Checkerboard Patterns in Layout Optimization",
journal = j-STRUCT-OPTIM,
volume = "10",
number = "",
pages = "40--45",
year = "1995",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Diaz:1995:NFP,
author = "A. R. D{\'\i}az and R. Lipton and Ciro A. Soto",
title = "A new formulation of the problem of optimum
reinforcement of {Reissner-Mindlin} plates",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "123",
number = "1-4",
pages = "121--139",
year = "1995",
CODEN = "CMMECC",
ISSN = "0045-7825",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
}
@Article{Diaz:1997:OML,
author = "A. R. D{\'\i}az and R. Lipton",
title = "Optimal Material Layout for 3{D} Elastic Structures",
journal = j-STRUCT-OPTIM,
volume = "13",
pages = "60--64",
year = "1997",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
bibdate = "Thu Oct 9 14:38:29 MDT 1997",
note = "Preliminary version in \cite{Lipton:1995:MFO}.",
}
@Article{Ding:1986:SOS,
author = "Y. Ding",
title = "Shape Optimization of Structures: {A} Literature
Survey",
journal = j-COMP-STRUCTURES,
volume = "24",
number = "6",
pages = "985--1004",
year = "1986",
CODEN = "CMSTCJ",
ISSN = "0045-7949",
}
@Article{Dolzmann:1995:ISE,
author = "G. Dolzmann and S. M{\"u}ller",
title = "The influence of surface energy on stress-free
microstructures in shape memory alloys",
journal = j-MECCANICA-MILAN,
volume = "30",
number = "5",
pages = "527--539",
year = "1995",
CODEN = "MECCB9",
ISSN = "0025-6455",
note = "Microstructure and phase transitions in solids (Udine,
1994)",
fjournal = "Meccanica. International Journal of the Italian
Association of Theoretical and Applied Mechanics",
}
@TechReport{Donato:1993:RCR,
author = "P. Donato",
title = "Recent controllability results for the wave equation
in domains with small holes",
institution = "Publications du Laboratoire d'Analyse Num{\'e}rique,
Universit{\'e} Pierre et Marie Curie",
year = "1993",
abstract = "An important problem in the application is the
controllability for perturbed systems. A special kind
of perturbed systems, depending on a small parameter
$\epsilon$, is the wave equation when the coefficients
are rapidly oscillating or when posed in periodically
perforated domains. A limit system (in the
homogenization theory sense) can be defined in some
cases. Then, two main questions can be formulated: (i)
does the exact controllability problem converges as $
\epsilon \longrightarrow 0$ to the control problem for
the limit system? (ii) is it possible to control
approximately the perturbated system in order to
obtain, as $\epsilon \longrightarrow 0$, exact
controllability at the limit? We present here a review
of some results for the exact and approximate
controllability answering to these questions.",
}
@Article{Drakhlin:19xx:CCF,
author = "M. E. Drakhlin and E. Stepanov",
title = "{$\Gamma$}-convergence for a Class of Functionals with
Deviating Argument",
year = "19xx",
note = "Submitted to J. Fcl. Analysis.",
abstract = "The paper deals with the problem of
$\Gamma$-convergence of functionals involving nonlocal
transformation of argument, in particular, the argument
deviation. The property of $\Gamma$-convergence of the
functionals is related with various types of
convergence of inner superposition (composition)
operators. The study is conducted in Orlicz spaces.
$\Gamma$-convergence of functionals with impulsive
constraints is also studied as one of the applications.
applications.",
ams = "49J25, 49J45, 49N25, 47A55, 47B38",
keywords = "Calculus of Variations, $\Gamma$-convergence,
Functional Differential Equation, Orlicz Space",
}
@Book{Dreyfus:1965:DPC,
author = "Stuart E. Dreyfus",
title = "Dynamic programming and the calculus of variations",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xix + 248",
year = "1965",
}
@Article{Dundurs:1989:CVR,
author = "J. Dundurs",
title = "Cavities vis-\`a-vis rigid inclusions and some related
general results in plane elasticity",
journal = j-J-APPL-MECH,
volume = "56",
number = "4",
pages = "786--790",
year = "1989",
CODEN = "JAMCAV",
ISSN = "0021-8936",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Series E. Journal of Applied Mechanics",
}
@Article{Dundurs:1997:EEM,
author = "J. Dundurs and I. Jasiuk",
title = "Effective elastic moduli of composite materials:
Reduced parameters dependence",
journal = j-APPL-MECH-REV,
volume = "50",
pages = "S39--S43",
year = "1997",
CODEN = "AMREAD",
ISSN = "0003-6900",
}
@Article{Dunn:1993:ERB,
author = "M. L. Dunn",
title = "Exact relations between the thermoelectroelastic
moduli of heterogeneous materials",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "441",
number = "1913",
pages = "549--557",
year = "1993",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Book{Duvaut:1976:IMP,
author = "G. Duvaut and J. L. Lions",
title = "Inequalities in mechanics and physics",
publisher = pub-SV,
address = pub-SV:adr,
year = "1976",
}
@Article{Dvorak:1990:UFH,
author = "G. J. Dvorak",
title = "On uniform fields in heterogeneous media",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "431",
number = "1881",
pages = "89--110",
year = "1990",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Dvorak:1992:SER,
author = "G. J. Dvorak",
title = "On some exact results in thermoplasticity of composite
materials",
journal = j-J-THERM-STRESS,
volume = "15",
number = "2",
pages = "211--228",
year = "1992",
CODEN = "JTSDAR",
ISSN = "0149-5739",
note = "Sixty-fifth Birthday of Bruno A. Boley Symposium, Part
2 (Atlanta, GA, 1991).",
fjournal = "Journal of Thermal Stresses. An International
Quarterly",
}
@Article{Dvorak:1992:TFA,
author = "G. J. Dvorak",
title = "Transformation field analysis of inelastic composite
materials",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "437",
number = "1900",
pages = "311--327",
year = "1992",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
MRnumber = "MR93e:73034b",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Dvorak:1992:TSU,
author = "G. J. Dvorak and Y. Benveniste",
fullauthor = "G. J. Dvorak and Yakov Benveniste",
title = "On transformation strains and uniform fields in
multiphase elastic media",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "437",
number = "1900",
pages = "291--310",
year = "1992",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
MRnumber = "MR93e:73034a",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@TechReport{Dvorak:1994:RNM,
author = "J. Dvo{\v{r}}{\'a}k",
title = "A Reliable Numerical Method for Computing Homogenized
Coefficients",
number = "MAT-Report 31",
institution = "Mathematical Institute, Danish Technical University",
address = "Lyngby, Denmark",
year = "1994",
abstract = "The problem of calculation of the effective
conductivity matrix of a periodic composite is treated
using convex analysis techniques. We show that results
of a conforming numerical solution of the primal
formulation of the homogenization formula converge to
the exact values from above, while numerical solutions
of the dual formulation converge from below. The
difference of the two numerical results provides a
reliable estimate of the numerical error in the
effective conductivities. We suggest a p-hierarchical
version of the FEM for the solution of the periodic PDE
problem that is involved; the numerical error estimate
provides a sound basis for adaptivity. We present
several numerical examples",
}
@Unpublished{Dvorak:19xx:HEC,
author = "J. Dvo{\v{r}}{\'a}k",
title = "Handbook of Extremal Composites for Linear Conduction.
One or Two Isotropic Phases in Single Inclusion
Microgeometries",
year = "19xx",
}
@Article{Dvorak:19xx:POM,
author = "J. Dvo{\v{r}{\'a}}k and J. Haslinger and Markku
Miettinen",
title = "On the problem of optimal material distribution",
journal = j-SIAM-J-APPL-MATH,
volume = "??",
number = "??",
pages = "??--??",
month = "??",
year = "19xx",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
note = "Submitted.",
}
@Article{Dykhne:1970:BEP,
author = "A. M. Dykhne",
title = "Conductivity of a two-dimensional two-phase system",
journal = j-J-EXP-THEOR-PHYS,
volume = "7",
pages = "110--116",
year = "1970",
CODEN = "JTPHES",
ISSN = "1090-6509, 1063-7761",
}
@Article{Dykhne:1971:CTD,
author = "A. M. Dykhne",
title = "Conductivity of a two-dimensional two-phase system",
journal = j-J-EXP-THEOR-PHYS,
volume = "32",
pages = "63--65",
year = "1971",
CODEN = "SPHJAR",
ISSN = "0038-5646",
}
@Article{Dyubin:1988:MGS,
author = "G. N. Dyubin and E. A. V. Cherkaeva",
title = "Measures that are generated by set functions",
journal = j-OPTIMIZATSIIA,
number = "44(61)",
pages = "143--154",
year = "1988",
ISSN = "0134-3998",
fjournal = "Akademiya Nauk SSSR. Sibirskoe Otdelenie. Institut
Matematiki. Optimizatsiya",
}
@Article{Efros:1976:CBC,
author = "A. L. Efros and B. I. Shklovskii",
title = "Critical behavior of conductivity and dielectric
constant near the metal-non-metal transition
threshold",
journal = j-PHYS-STATUS-SOLIDI-B-BASIC-RES,
volume = "76",
pages = "475--485",
year = "1976",
CODEN = "PSSBBD",
ISSN = "0370-1972",
}
@Book{Ekeland:1974:ACP,
author = "I. Ekeland and R. Temam",
title = "Analyse convexe et probl{\`e}mes variationnels",
publisher = pub-DUNOD,
address = pub-DUNOD:adr,
pages = "x + 340",
year = "1974",
MRnumber = "MR57:3931a",
note = "Collection \'Etudes Math{\'e}matiques.",
}
@Book{Ekeland:1976:CAV,
author = "I. Ekeland and R. Temam",
title = "Convex analysis and variational problems",
publisher = pub-NH,
address = pub-NH:adr,
pages = "ix + 402",
year = "1976",
note = "Translated from the French, Studies in Mathematics and
its Applications, Vol. 1.",
}
@Article{Elcrat:1997:IPF,
author = "A. Elcrat and Vassilis G. Papanicolaou",
title = "On the inverse problem of a fourth-order self-adjoint
binomial operator",
journal = j-SIAM-J-MATH-ANA,
volume = "28",
number = "4",
pages = "886--896",
year = "1997",
CODEN = "SJMAAH",
ISSN = "0036-1410",
MRnumber = "MR98f:34015",
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Eldiwany:1986:RIM,
author = "B. H. Eldiwany and L. T. Wheeler",
title = "On rigid inclusions of minimum stress concentration",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "34",
number = "1",
pages = "19--28",
year = "1986",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Book{Elsgolts:1973:DEC,
author = "L. Elsgolts",
title = "Differential equations and the calculus of
variations",
publisher = pub-MIR,
address = pub-MIR:adr,
pages = "440",
year = "1973",
note = "Translated from the Russian by G. Yankovsky.",
}
@Article{Ericksen:1980:SPT,
author = "J. Ericksen",
title = "Some phase transitions in crystals",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "73",
number = "",
pages = "99--124",
year = "1980",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Ericksen:1986:CRT,
author = "J. Ericksen",
title = "Constitutive theory for some constrained elastic
crystals",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "22",
number = "",
pages = "951--964",
year = "1986",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Ericksen:1991:KCC,
author = "J. L. Ericksen",
title = "On kinematic conditions of compatibility",
journal = j-J-ELAST,
volume = "26",
number = "1",
pages = "65--74",
year = "1991",
CODEN = "JELSAY",
ISSN = "0374-3535",
MRnumber = "MR92j:73005",
fjournal = "Journal of Elasticity",
}
@Article{Ericksen:1992:RNP,
author = "J. L. Ericksen",
title = "Reversible and nondissipative processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "45",
number = "4",
pages = "545--554",
year = "1992",
CODEN = "QJMMAV",
ISSN = "0033-5614",
MRnumber = "MR94a:80004",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
}
@Book{Ericksen:1998:ITS,
author = "J. L. Ericksen",
title = "Introduction to the thermodynamics of solids",
publisher = pub-SV,
address = "New York",
edition = "Revised",
pages = "xii + 189",
year = "1998",
ISBN = "0-387-98364-3",
MRnumber = "MR98k:73009",
}
@Article{Eshelby:1957:DEF,
author = "J. D. Eshelby",
title = "The determination of the elastic field of an
ellipsoidal inclusion, and related problems",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "241",
number = "",
pages = "376--396",
year = "1957",
}
@Article{Eshelby:1959:EFE,
author = "J. D. Eshelby",
title = "The elastic field outside an ellipsoidal inclusion",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "252",
pages = "561--569",
year = "1959",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@InCollection{Eshelby:1961:EII,
author = "J. D. Eshelby",
booktitle = "Progress in Solid Mechanics, Vol. II",
title = "Elastic inclusions and inhomogeneities",
publisher = pub-NH,
address = pub-NH:adr,
pages = "87--140",
year = "1961",
}
@Article{Eshelby:1975:EEM,
author = "J. D. Eshelby",
title = "The elastic energy-momentum tensor",
journal = j-J-ELAST,
volume = "5",
number = "3-4",
pages = "321--335",
year = "1975",
CODEN = "JELSAY",
ISSN = "0374-3535",
note = "Special issue dedicated to A. E. Green",
}
@Book{Ewing:1969:CVA,
author = "G. M. Ewing",
title = "Calculus of variations with applications",
publisher = "W. W. Norton \& Co. Inc.",
address = "New York",
pages = "xii + 343",
year = "1969",
}
@Book{Ewing:1985:CVA,
author = "G. M. Ewing",
title = "Calculus of variations with applications",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "viii + 343",
year = "1985",
ISBN = "0-486-64856-7",
note = "Corrected reprint of the 1969 original.",
}
@Article{Fannjiang:1994:CED,
author = "A. Fannjiang and G. Papanicolaou",
title = "Convection enhanced diffusion for periodic flows",
journal = j-SIAM-J-APPL-MATH,
volume = "54",
number = "2",
pages = "333--408",
year = "1994",
CODEN = "SMJMAP",
ISSN = "0036-1399",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Fannjiang:1996:DT,
author = "A. Fannjiang and G. Papanicolaou",
title = "Diffusion in turbulence",
journal = j-PROBAB-THEORY-RELAT-FIELDS,
volume = "105",
number = "3",
pages = "279--334",
year = "1996",
CODEN = "PTRFEU",
ISSN = "0178-8051",
MRnumber = "MR98d:60156",
fjournal = "Probability Theory and Related Fields",
}
@Article{Fannjiang:1997:CED,
author = "A. Fannjiang and G. Papanicolaou",
title = "Convection-enhanced diffusion for random flows",
journal = j-J-STAT-PHYS,
volume = "88",
number = "5-6",
pages = "1033--1076",
year = "1997",
CODEN = "JSTPSB",
ISSN = "0022-4715",
MRnumber = "MR1478061",
fjournal = "Journal of Statistical Physics",
}
@InCollection{Fannjiang:1998:ETC,
author = "A. Fannjiang and L. Ryzhik and G. Papanicolaou",
booktitle = "Recent advances in partial differential equations
Venice 1996",
title = "Evolution of trajectory correlations in steady random
flows",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "105--130",
year = "1998",
MRnumber = "MR1492694",
}
@Article{Fedorov:1983:COO,
author = "A. V. Fedorov and A. V. Cherkaev",
title = "Choosing of optimal orientation of axes of elastic
symmetry of orthotropic plate",
journal = j-MECH-SOLIDS,
volume = "3",
pages = "135--142",
year = "1983",
CODEN = "MESOBN",
ISSN = "0025-6544",
}
@Article{Fenchel:1949:CCF,
author = "W. Fenchel",
title = "On conjugate convex functions",
journal = j-CAN-J-MATH,
volume = "1",
pages = "73--77",
year = "1949",
CODEN = "CJMAAB",
ISSN = "0008-414X",
}
@InCollection{Fenchel:1983:CTA,
author = "W. Fenchel",
booktitle = "Convexity and its applications",
title = "Convexity through the ages",
publisher = "Birkh{\"a}user",
address = "Basel",
pages = "120--130",
year = "1983",
}
@Article{Filippov:1959:CQT,
author = "A. F. Filippov",
title = "On certain questions in the theory of optimal
control",
journal = "Vestnik Moskovskogo Universiteta. Matematica i
Astronomia",
volume = "2",
pages = "25--32",
year = "1959",
MRclass = "93.40.",
MRnumber = "26\#7469",
note = "See also paper of same name in J. SIAM Control Ser. A,
{\bf 1}, 1962, 76--84.",
}
@Article{FinziVita:1996:QLR,
author = "S. {Finzi Vita} and F. Murat and N. A.
Tchou",
fullauthor = "Stefano {Finzi Vita} and F. Murat and Nicoletta A.
Tchou",
title = "Quasi-linear relaxed {Dirichlet} problems",
journal = j-SIAM-J-MATH-ANA,
volume = "27",
number = "4",
pages = "977--996",
year = "1996",
CODEN = "SJMAAH",
ISSN = "0036-1410",
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Firoozye:1991:OUT,
author = "N. B. Firoozye",
title = "Optimal use of the translation method and relaxations
of variational problems",
journal = j-COMM-PURE-APPL-MATH,
volume = "44",
number = "6",
pages = "643--678",
year = "1991",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@InCollection{Firoozye:1993:GPR,
author = "N. B. Firoozye and R. V. Kohn",
editor = "D. Kinderlehrer and R. James and M. Luskin and J. L.
Ericksen",
booktitle = "Microstructure and phase transition",
title = "Geometric parameters and the relaxation of multiwell
energies",
publisher = pub-SV,
address = "New York",
pages = "85--109",
year = "1993",
}
@Article{Fisher:1986:CFO,
author = "M. E. Fisher and G. W. Milton",
title = "Classifying first-order phase transitions",
journal = j-PHYSICA-A,
volume = "138",
number = "1-2",
pages = "22--54",
year = "1986",
CODEN = "PHYSAG",
ISSN = "0378-4371",
fjournal = "Physica. A. Europhysics Journal",
}
@Article{Fisher:1987:ECF,
author = "M. E. Fisher and G. W. Milton",
title = "Erratum: ``{Classifying} first-order phase
transitions'' [{Phys}.\ {A} {\bf 138} (1986), no.\ 1,
22--54; {MR} 87k:82052]",
journal = j-PHYSICA-A,
volume = "142",
number = "1-3",
pages = "649",
year = "1987",
CODEN = "PHYSAG",
ISSN = "0378-4371",
fjournal = "Physica. A. Europhysics Journal",
}
@Article{Foiaedlas:1980:OTG,
author = "C. Foia{\cedla{s}} and L. Tartar",
fullauthor = "Ciprian Foia{\cedla{s}} and L. Tartar",
title = "Op{\'e}rateurs de {Toeplitz} g{\'e}n{\'e}ralis{\'e}s
et homog{\'e}n{\'e}isation",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "291",
number = "1",
pages = "A15--A18",
year = "1980",
CODEN = "CHASAP",
ISSN = "0151-0509",
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
}
@InProceedings{Folgado:1995:LDP,
author = "J. Folgado and H. Rodrigues and J. M. Guedes",
editor = "N. Olhoff and G. I. N. Rozvany",
booktitle = "Structural and Multidisciplinary Optimization",
title = "Layout Design of Plate Reinforcements with a Buckling
Load Criterion",
organization = "ISSMO",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "659--666",
month = "",
year = "1995",
confaddress = "Goslar, Germany",
}
@Article{Fonseca:1987:VME,
author = "I. Fonseca",
title = "Variational methods for elastic crystals",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "97",
number = "3",
pages = "189--220",
year = "1987",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Fonseca:1989:DPE,
author = "I. Fonseca and L. Tartar",
title = "The displacement problem for elastic crystals",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "113",
number = "1-2",
pages = "159--180",
year = "1989",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Fonseca:1989:GTP,
author = "I. Fonseca and L. Tartar",
title = "The gradient theory of phase transitions for systems
with two potential wells",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "111",
number = "1-2",
pages = "89--102",
year = "1989",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Fonseca:1989:LQE,
author = "I. Fonseca",
title = "The lower quasiconvex envelope of the stored energy
function for an elastic crystal",
journal = j-J-MATH-PURES-APPL,
volume = "67",
number = "2",
pages = "175--195",
year = "1988",
CODEN = "JMPAAM",
ISSN = "0021-7824",
fjournal = "Journal de Math\'ematiques Pures et Appliqu\'ees.
Neuvi\`eme S\'erie",
}
@Article{Fonseca:1989:PTE,
author = "I. Fonseca",
title = "Phase transitions of elastic solid materials",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "107",
number = "3",
pages = "195--223",
year = "1989",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Fonseca:1992:LSS,
author = "I. Fonseca",
title = "Lower semicontinuity of surface energies",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "120",
number = "1-2",
pages = "99--115",
year = "1992",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Fonseca:1994:EFD,
author = "I. Fonseca and D. Kinderlehrer and P. Pedregal",
title = "Energy functionals depending on elastic strain and
chemical composition",
journal = j-CALC-VAR-PARTIAL-DIFFER-EQU,
volume = "2",
number = "3",
pages = "283--313",
year = "1994",
ISSN = "0944-2669",
fjournal = "Calculus of Variations and Partial Differential
Equations",
}
@Article{Fortuin:1972:RCM,
author = "C. Fortuin and P. Kasteleyn",
title = "On the random-cluster model. {I}. {Introduction} and
relation to other models",
journal = j-PHYSICA,
volume = "57",
pages = "536--564",
year = "1972",
CODEN = "PHYSAG",
ISSN = "0031-8914",
}
@Book{Fox:1987:ICV,
author = "C. Fox",
title = "An introduction to the calculus of variations",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 271",
year = "1987",
ISBN = "0-486-65499-0",
note = "Reprint of the 1963 edition.",
}
@Article{Francfort:1986:HOB,
author = "G. A. Francfort and F. Murat",
title = "Homogenization and Optimal Bounds in Linear
Elasticity",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "94",
number = "4",
pages = "307--334",
year = "1986",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Francfort:1987:OBCa,
author = "G. A. Francfort and G. W. Milton",
title = "Optimal bounds for conduction in two-dimensional,
multiphase, polycrystalline media",
journal = j-J-STAT-PHYS,
volume = "46",
number = "1-2",
pages = "161--177",
year = "1987",
CODEN = "JSTPSB",
ISSN = "0022-4715",
fjournal = "Journal of Statistical Physics",
}
@InProceedings{Francfort:1987:OBCb,
author = "G. A. Francfort and F. Murat",
booktitle = "Nonclassical continuum mechanics (Durham, 1986)",
title = "Optimal bounds for conduction in two-dimensional,
two-phase, anisotropic media",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "197--212",
year = "1987",
}
@Article{Francfort:1991:CEM,
author = "G. A. Francfort and L. Tartar",
title = "Comportement effectif d'un m{\'e}lange de
mat{\'e}riaux {\'e}lastiques isotropes ayant le
m{\^{}e}me module de cisaillement",
journal = j-C-R-ACAD-SCI-PARIS,
volume = "312",
number = "3",
pages = "301--307",
year = "1991",
CODEN = "CASMEI",
ISSN = "0764-4442",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences.
S{\'e}rie I. Math{\'e}matique",
}
@Article{Francfort:1992:OED,
author = "G. A. Francfort and F. Murat",
title = "Oscillations and energy densities in the wave
equation",
journal = j-COMM-PARTIAL-DIFF-EQNS,
volume = "17",
number = "11-12",
pages = "1785--1865",
year = "1992",
CODEN = "CPDIDZ",
ISSN = "0360-5302",
fjournal = "Communications in Partial Differential Equations",
}
@Article{Francfort:1993:SDE,
author = "G. A. Francfort and J. Marigo",
title = "Stable damage evolution in a brittle continuous
medium",
journal = j-EUR-J-MECH-A-SOLIDS,
volume = "12",
pages = "149--189",
year = "1993",
CODEN = "EJASEV",
ISSN = "0997-7538",
}
@Article{Francfort:1994:CEH,
author = "G. A. Francfort and S. M{\"u}ller",
title = "Combined Effects of Homogenization and Singular
Perturbations in Elasticity",
journal = j-J-REINE-ANGEW-MATH,
volume = "454",
pages = "1--35",
year = "1994",
CODEN = "JRMAA8",
ISSN = "0075-4102",
MRclass = "73B27 (35B27 49J45 73C50 73V25)",
MRnumber = "95h:73007",
abstract = "The combined effects of small heterogeneities and
higher order perturbations for both linear and fully
nonlinear elastic materials are discussed. In the
linear case the theory of $H$-convergence is extended
to allow for the inclusion of higher order
perturbations. As an application the case of periodic
heterogeneities is studied in detail. Specifically it
is shown that the limiting problem corresponding to $ -
\mbox{div} A (x/\epsilon^\gamma) \mbox{grad} u^\epsilon
+ \epsilon^2 \nabla^2 u^\epsilon = f$ is given by $ -
\mbox{div} A^0 \mbox{grad} \ u = f$, where $A^0$ equals
the classical $H$-limit if $\gamma \le 1$ (i.e. if the
length scale of the heterogeneities is large compared
to the scale $\epsilon$ introduced by the
perturbation), while $A^0$ is the average of $A$ is
$\gamma \ge 1$. In the intermediate case $\gamma = 1$
both the heterogeneities and the higher order
perturbation contribute to $A^0$. Analogous results are
established in the nonlinear setting by studying the
$\Gamma$-limit of the functionals $\int W
(x/\epsilon^\gamma, \mbox{grad} \ u) + \epsilon^2
{(\nabla \ u)}^2$",
ams = "Subject 35B25, 73C40 (49B21, 73C60)",
}
@Article{Francfort:1994:SCE,
author = "G. A. Francfort and G. W. Milton",
title = "Sets of conductivity and elasticity tensors stable
under lamination",
journal = j-COMM-PURE-APPL-MATH,
volume = "47",
number = "3",
pages = "257--279",
year = "1994",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Francfort:1995:FOM,
author = "G. A. Francfort and F. Murat and L. Tartar",
title = "Fourth-order moments of nonnegative measures on
${S}\sp2$ and applications",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "131",
number = "4",
pages = "305--333",
year = "1995",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@InCollection{Francfort:1997:OCC,
author = "F. Murat and G. A. Francfort",
booktitle = "Non-classical Continuum Mechanics (Edited by R. J.
Knops and A. A. Laccey), London Mathematical Society
Lecture Notes Series 122",
title = "Optimal construction for conduction in two-dimensional
two-phase, anisotropic media",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "197--212",
year = "1997",
}
@TechReport{Francu:19xx:WCO,
author = "J. Francu",
fullauthor = "Jan Francu",
title = "Weakly Continuous Operators - Applications to
Differential Equations",
year = "19xx",
note = "To appear.",
abstract = "The paper is a supplement to a survey by J. Francu:
Monotone operators, A survey directed to differential
equations, Aplikace Matematiky, 35(1990), 257-301. An
abstract existence theorem for equation $Au = b$ with
coercive weakly continuous operator is proved. The
application to boundary value problems for differential
equations is illustrated on two examples. Although this
generalization of monotone operator theory is not as
general as M-condition, it is sufficient for many
technical applications.",
ams = "35-02, 35A05, 35F30, 76D05",
keywords = "monotone operators, weakly continuous operators,
existence theorems, boundary value problems for
differential equations, heat conduction equation,
Navier-{Stokes} equations",
}
@Article{Friedman:1992:TMM,
author = "A. Friedman and P. Knabner",
title = "A Transport Model with Micro- and Macro-Structure",
journal = j-J-DIFFER-EQU,
volume = "98",
number = "2",
pages = "328--354",
year = "1992",
CODEN = "JDEQAK",
ISSN = "0022-0396",
MRclass = "35Q35 (76S05 80A30)",
MRnumber = "93g:35114",
abstract = "In this paper we consider solute transport through
porous media where the chemical species undergoes a
chemical process through the surface of the porous
skeleton. The problem is modeled by a system of
differential equations for the macro-concentration $u =
u(x,t)$ and the micro-concentration $u' = u'(x,x',t)$.
We prove existence and uniqueness, and some properties
of the set with positive concentration.",
oldjournal = "Schwerpunktprogramm der Deutschen
Forschungsgemeinschaft",
oldnumber = "246",
oldyear = "1990",
}
@Article{Fu:1998:FSM,
author = "Y. Fu and K. J. Klimkowski and G. J. Rodin and E.
Berger and J. C. Browne and J. K. Singer and R. A. {van
de Geijn} and K. S. Vemaganti",
title = "A Fast Solution Method for Three-Dimensional
Many-Particle Problems of Linear Elasticity",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "42",
pages = "1215--1229",
year = "1998",
CODEN = "IJNMBH",
ISSN = "0029-5981",
}
@Book{Fuchs:1994:TCV,
author = "M. Fuchs",
title = "Topics in the calculus of variations",
publisher = "Friedr. Vieweg \& Sohn",
address = "Braunschweig",
pages = "viii + 145",
year = "1994",
ISBN = "3-528-06623-7",
}
@Article{Fuchs:1996:UCA,
author = "M. B. Fuchs and S. Hakim",
title = "Improved Multivariate Reanalysis of Structures Based
on the Structural Variation Method",
journal = j-MECHAN-STRUCT-MACH,
volume = "24",
number = "1",
pages = "51--70",
year = "1996",
CODEN = "MSMAEI",
ISSN = "0890-5452",
fjournal = "",
}
@Book{Gabasov:1973:OOU,
author = "R. Gabasov and F. M. Kirillova",
title = "{Singular optimal controls}",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
pages = "256",
year = "1973",
note = "Monographs in Theoretical Foundations of Technical
Cybernetics.",
}
@Article{Galka:1992:HT,
author = "A. Ga{\l}ka and J. J. Telega and R. Wojnar",
title = "Homogenization and thermopiezoelectricity",
journal = j-MECH-RESEARCH-COMM,
volume = "19",
pages = "315--324",
year = "1992",
CODEN = "MRCOD2",
ISSN = "0093-6413",
}
@InProceedings{Galka:1992:HTS,
author = "A. Ga{\l}ka and J. J. Telega and R. Wojnar",
editor = "W. Kosi{\'n}ski and others",
booktitle = "Thermodynamics and Kinetic Theory",
title = "Homogenization of a thermoelastic solid in the
presence of diffusion",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "35--48",
year = "1992",
}
@Article{Galka:1994:THE,
author = "A. Ga{\l}ka and J. J. Telega and R. Wojnar",
title = "Thermodiffusion in heterogeneous elastic solids and
homogenization",
journal = j-ARCH-MECH,
volume = "46",
pages = "267--314",
year = "1994",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Gamkrelidze:1962:SOS,
author = "R. V. Gamkrelidze",
title = "On sliding optimal states",
journal = j-DOKL-AKAD-NAUK,
volume = "143",
pages = "1243--1245",
year = "1962",
CODEN = "DANKAS",
ISSN = "0002-3264",
}
@Article{Gamkrelidze:1985:SMO,
author = "R. V. Gamkrelidze",
title = "Sliding modes in optimal control theory",
journal = j-PROC-STEKLOV-INST-MATH,
volume = "169",
pages = "180--193, 255",
year = "1985",
CODEN = "TMISAF",
ISSN = "0371-9685",
note = "Topology, ordinary differential equations, dynamical
systems.",
fjournal = "Akademiya Nauk Soyuza Sovetskikh Sotsialisticheskikh
Respublik. Trudy Matematicheskogo Instituta imeni V. A.
Steklova",
}
@Article{Gawlinski:1981:CPT,
author = "E. T. Gawlinski and H. E. Stanley",
title = "Continuum percolation in two dimensions: {Monte}
{Carlo} tests of scaling and universality for
non-interacting discs",
journal = j-J-PHYS-A,
volume = "14",
pages = "L291--L299",
year = "1981",
CODEN = "JPHAC5",
ISSN = "0305-4470",
}
@Article{Gebelprime:1989:EOC,
author = "M. Gebel{\cprime} and U. {\"E}. Ra{\u\i}tum",
title = "Extension of optimal control problems",
journal = j-MATH-NACHR,
volume = "143",
pages = "291--302",
year = "1989",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
fjournal = "Mathematische Nachrichten",
}
@Book{Gelfand:1963:CV,
author = "I. M. Gelfand and S. V. Fomin",
title = "Calculus of variations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "vii + 232",
year = "1963",
note = "Revised English edition translated and edited by
Richard A. Silverman.",
}
@Book{Gelfand:1965:LLA,
author = "I. M. Gelfand",
editor = "",
title = "Lectures on Linear Algebra",
volume = "",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
edition = "",
month = "",
year = "1965",
series = "",
}
@Article{Gerard:1991:MDM,
author = "Patrick G{\'e}rard",
title = "Microlocal defect measures",
journal = j-COMM-PARTIAL-DIFF-EQNS,
volume = "16",
number = "11",
pages = "1761--1794",
year = "1991",
CODEN = "CPDIDZ",
ISSN = "0360-5302",
fjournal = "Communications in Partial Differential Equations",
}
@InCollection{Gerard:1991:MSC,
author = "P. G{\'e}rard",
booktitle = "S{\'e}minaire sur les \'Equations aux D{\'e}riv{\'e}es
Partielles, 1990--1991",
title = "Mesures semi-classiques et ondes de {Bloch}",
publisher = "{\'E}cole Polytech.",
address = "Palaiseau, France",
pages = "Exp.\ No.\ XVI, 19",
year = "1991",
xxnote = "Check pages??.",
}
@Article{Geymonat:1993:HNE,
author = "G. Geymonat and S. M{\"u}ller and N. Triantafyllidis",
title = "Homogenization of non-linearly elastic materials,
microscopic bifurcation and macroscopic loss of
rank-one convexity",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "122",
number = "3",
pages = "231--290",
year = "1993",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Book{Giaquinta:1983:MIC,
author = "M. Giaquinta",
title = "Multiple integrals in the calculus of variations and
nonlinear elliptic systems",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "vii + 297",
year = "1983",
ISBN = "0-691-08330-4; 0-691-08331-2",
}
@TechReport{Gibiansky:1984:DCP,
author = "L. V. Gibiansky and A. V. Cherkaev",
title = "Design of composite plates of extremal rigidity",
type = "Report",
number = "914",
institution = "Ioffe Physico-technical Institute, Acad of Sc, USSR",
address = "Leningrad, USSR",
year = "1984",
note = "English translation in \cite{Gibiansky:1997:DCP}",
}
@TechReport{Gibiansky:1987:MCE,
author = "L. V. Gibiansky and A. V. Cherkaev",
title = "Microstructures of composites of extremal rigidity and
exact estimates of the associated energy density",
type = "Report",
number = "1115",
institution = "Ioffe Physico-Technical Institute, Acad of Sc, USSR",
address = "Leningrad, USSR",
year = "1987",
note = "English translation in \cite{Gibiansky:1997:MCE}.",
}
@TechReport{Gibiansky:1988:DCP,
author = "L. V. Gibiansky and A. V. Cherkaev",
title = "The set of tensor pairs of dielectric and magnetic
permeabilities of two-phase composites",
number = "1286",
institution = "Ioffe Physico-technical Institute, Acad of Sc, USSR",
address = "Leningrad, USSR",
year = "1988",
note = "English translation in \cite{Cherkaev:1992:ECB}",
}
@Article{Gibiansky:1988:OFH,
author = "L. V. Gibiansky and K. A. Lurie and A. V. Cherkaev",
title = "Optimal focusing of heat flow by heterogeneous heat
conducting media (thermolens problem)",
journal = j-Z-TEH-FIZ,
volume = "58",
number = "1",
pages = "67--74",
year = "1988",
CODEN = "ZTEFA3",
ISSN = "0044-4642",
}
@Article{Gibiansky:1993:EVM,
author = "L. V. Gibiansky and G. W. Milton",
title = "On the effective viscoelastic moduli of two-phase
media: {I}. {Rigorous} bounds on the complex bulk
modulus",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "440",
number = "1908",
pages = "163--188",
year = "1993",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Gibiansky:1993:LBC,
author = "L. V. Gibiansky and S. Torquato",
title = "Link between the conductivity and elastic moduli of
composite materials",
journal = j-PHYS-REV-LET,
volume = "71",
number = "18",
pages = "2927--2930",
year = "1993",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Gibiansky:1995:GPB,
author = "L. V. Gibiansky and S. Torquato",
title = "Geometrical-parameter bounds on the effective moduli
of composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "43",
number = "10",
pages = "1587--1613",
year = "1995",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Gibiansky:1995:RLB,
author = "L. V. Gibiansky and S. Torquato",
title = "Rigorous link between the conductivity and elastic
moduli of fiber-reinforced composite materials",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "353",
pages = "243--278",
year = "1995",
CODEN = "PTMSFB",
ISSN = "1364-503X",
}
@Article{Gibiansky:1996:BEM,
author = "L. V. Gibiansky and S. Torquato",
title = "Bounds on the effective moduli of cracked materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "44",
number = "2",
pages = "233--242",
year = "1996",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Gibiansky:1996:CBC,
author = "L. V. Gibiansky and S. Torquato",
title = "Connection between the conductivity and bulk modulus
of isotropic composite materials",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "452",
number = "1945",
pages = "253--283",
year = "1996",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@InCollection{Gibiansky:1997:DCP,
author = "L. V. Gibiansky and A. V. Cherkaev",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "Design of Composite Plates of Extremal Rigidity",
volume = "31",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "95--137",
year = "1997",
note = "Translation. The original publication in
\cite{Gibiansky:1984:DCP}",
series = "Progress in nonlinear differential equations and their
applications",
xxbooktitle = "Topics in the mathematical modeling of composite
materials",
}
@InCollection{Gibiansky:1997:MCE,
author = "L. V. Gibiansky and A. V. Cherkaev",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "Microstructures of composites of extremal rigidity and
exact bounds on the associated energy density",
volume = "31",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "273--317",
year = "1997",
note = "Translation. The original publication is in
\cite{Gibiansky:1987:MCE}.",
series = "Progress in nonlinear differential equations and their
applications",
xxbooktitle = "Topics in the mathematical modeling of composite
materials",
}
@Article{Gibiansky:1997:TEI,
author = "L. V. Gibiansky and S. Torquato",
title = "Thermal expansion of isotropic multiphase composites
and polycrystals",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "7",
pages = "1223--1252",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Gibiansky:1997:UHT,
author = "L. V. Gibiansky and S. Torquato",
title = "On the use of homogenization theory to design optimal
piezocomposites for hydrophone applications",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "5",
pages = "689--708",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@TechReport{Gibiansky:1998:MCE,
author = "L. V. Gibiansky and O. Sigmund",
title = "Multiphase composites with extremal bulk modulus",
number = "600",
institution = "DCAMM",
address = "DTU, Lyngby, Denmark",
month = dec,
year = "1998",
}
@Article{Gibiansky:1998:NMG,
author = "L. V. Gibiansky and S. Torquato",
title = "New method to generate three-point bounds on effective
properties of composites: application to
viscoelasticity",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "46",
number = "4",
pages = "749--783",
year = "1998",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Giorgi:1994:CSS,
author = "E. {De Giorgi}",
title = "On the convergence of solutions of some evolution
differential equations",
journal = j-SET-VALUED-ANAL,
volume = "2",
number = "1-2",
pages = "175--182",
year = "1994",
CODEN = "SVANEG",
ISSN = "0927-6947",
note = "Set convergence in nonlinear analysis and
optimization",
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
}
@InCollection{Giorgi:1994:NIC,
author = "E. {De Giorgi}",
booktitle = "Motion by mean curvature and related topics (Trento,
1992)",
title = "New ideas in calculus of variations and geometric
measure theory",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
pages = "63--69",
year = "1994",
}
@Article{Golden:1983:BEP,
author = "K. Golden and G. Papanicolaou",
title = "Bounds for effective parameters of heterogeneous media
by analytic continuation",
journal = j-COMMUN-MATH-PHYS,
volume = "90",
number = "4",
pages = "473--491",
year = "1983",
CODEN = "CMPHAY",
ISSN = "0010-3616",
fjournal = "Communications in Mathematical Physics",
}
@Article{Golden:1985:BEP,
author = "K. Golden and G. Papanicolaou",
title = "Bounds for effective parameters of multicomponent
media by analytic continuation",
journal = j-J-STAT-PHYS,
volume = "40",
number = "5-6",
pages = "655--667",
year = "1985",
CODEN = "JSTPSB",
ISSN = "0022-4715",
fjournal = "Journal of Statistical Physics",
}
@Article{Golden:1986:BCP,
author = "K. Golden",
title = "Bounds on the complex permittivity of a multicomponent
material",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "34",
number = "4",
pages = "333--358",
year = "1986",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@InCollection{Golden:1989:CRR,
author = "K. Golden",
editor = "R. V. Kohn and G. W. Milton",
booktitle = "Random media and composites (Leesburg, VA, 1988)",
title = "Convexity in random resistor networks",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "149--170",
year = "1989",
}
@Article{Golden:1990:CEI,
author = "K. Golden",
title = "Convexity and exponent inequalities for conduction
near percolation",
journal = j-PHYS-REV-LET,
volume = "65",
number = "24",
pages = "2923--2926",
year = "1990",
CODEN = "PRLTAO",
ISSN = "0031-9007",
fjournal = "Physical Review Letters",
}
@Article{Golden:1990:DBE,
author = "K. Golden and S. Goldstein and J. L. Lebowitz",
title = "Discontinuous behavior of effective transport
coefficients in quasiperiodic media",
journal = j-J-STAT-PHYS,
volume = "58",
number = "3-4",
pages = "669--684",
year = "1990",
CODEN = "JSTPSB",
ISSN = "0022-4715",
fjournal = "Journal of Statistical Physics",
}
@InCollection{Golden:1991:CTQ,
author = "K. Golden",
booktitle = "Mathematics of random media (Blacksburg, VA, 1989)",
title = "Classical transport in quasiperiodic media",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "359--373",
year = "1991",
}
@Article{Golden:1995:SMC,
author = "K. M. Golden",
title = "Statistical mechanics of conducting phase
transitions",
journal = j-J-MATH-PHYS,
volume = "36",
number = "10",
pages = "5627--5642",
month = oct,
year = "1995",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
fjournal = "Journal of Mathematical Physics",
}
@Article{Golden:1997:CBT,
author = "K. M. Golden",
title = "Critical behavior of transport in lattice and
continuum percolation models",
journal = j-PHYS-REV-LET,
volume = "78",
number = "20",
pages = "3935--3938",
year = "1997",
CODEN = "PRLTAO",
ISSN = "0031-9007",
fjournal = "Physical Review Letters",
}
@InCollection{Golden:1997:PMP,
author = "K. Golden",
booktitle = "Homogenization and porous media",
title = "Percolation models for porous media",
publisher = pub-SV,
address = "New York",
pages = "27--43, 259--275",
year = "1997",
}
@Article{Golden:19xx:CBT,
author = "K. Golden",
title = "Critical behaviour of transport in disordered
materials",
journal = j-PHYS-REV-LET,
volume = "??",
number = "??",
pages = "??--??",
month = "??",
year = "19xx",
CODEN = "PRLTAO",
ISSN = "0031-9007",
note = "Submitted.",
}
@Book{Goldstine:1980:HCV,
author = "Herman H. Goldstine",
title = "A history of the calculus of variations from the 17th
through the 19th century",
publisher = pub-SV,
address = "New York",
pages = "xviii + 410",
year = "1980",
ISBN = "0-387-90521-9",
}
@Article{Goodman:1986:NSR,
author = "J. Goodman and R. V. Kohn and L. Reyna",
title = "Numerical study of a relaxed variational problem from
optimal design",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "57",
pages = "107--127",
year = "1986",
CODEN = "CMMECC",
ISSN = "0045-7825",
}
@Article{Grabovsky:1993:GCT,
author = "Y. Grabovsky",
title = "The {G-closure} of two well-ordered anisotropic
conductors",
journal = j-PROC-R-SOC-EDINB,
volume = "123A",
pages = "423--432",
year = "1993",
CODEN = "PRSEAE",
ISSN = "0080-4541",
}
@Article{Grabovsky:1995:AVM,
author = "Y. Grabovsky and R. V. Kohn",
title = "Anisotropy of the {Vigdergauz} microstructure",
journal = j-J-APPL-MECH,
volume = "62",
number = "4",
pages = "1063--1065",
year = "1995",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@Article{Grabovsky:1995:MMEa,
author = "Y. Grabovsky and R. V. Kohn",
title = "Microstructures minimizing the energy of a two phase
elastic composite in two space dimensions. {I}: the
confocal ellipse construction",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "43",
number = "6",
pages = "933--947",
year = "1995",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Grabovsky:1995:MMEb,
author = "Y. Grabovsky and R. V. Kohn",
title = "Microstructures minimizing the energy of a two phase
elastic composite in two space dimensions. {II}: the
{Vigdergauz} microstructure",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "43",
number = "6",
pages = "949--972",
year = "1995",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Grabovsky:1995:NAQ,
author = "Y. Grabovsky",
title = "Nonsmooth analysis and quasi-convexification in
elastic energy minimization problems",
journal = j-STRUCT-OPTIM,
volume = "10",
number = "3/4",
pages = "217--221",
month = dec,
year = "1995",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Grabovsky:1995:TDG,
author = "Y. Grabovsky",
title = "{``Two-dimensional grained composites of extreme
rigidity''}, by {S. Vigdergauz} --- Discussion by {Y.
Grabovsky} with author's closure",
journal = j-J-APPL-MECH,
volume = "62",
number = "2",
pages = "550",
year = "1995",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@Article{Grabovsky:1996:BEM,
author = "Y. Grabovsky",
title = "Bounds and extremal microstructures for two-component
composites: {A} unified treatment based on the
translation method",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "452",
number = "1947",
pages = "945--952",
year = "1996",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@Article{Grabovsky:1996:ESO,
author = "Y. Grabovsky",
title = "Explicit solution of an optimal design problem with
non-affine boundary conditions",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "452",
number = "1947",
pages = "919--944",
year = "1996",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@InProceedings{Grabovsky:1998:ERC,
author = "Y. Grabovsky and G. W. Milton",
booktitle = "Proceedings of the International Congress of
Mathematicians, (Berlin, 1998)",
title = "Exact relations for composites: towards a complete
solution",
journal = j-DOC-MATH,
volume = "III",
pages = "623--632 (electronic)",
year = "1998",
ISSN = "1431-0643",
fjournal = "Documenta Mathematica",
}
@Article{Grabovsky:1998:ERE,
author = "Y. Grabovsky and D. S. Sage",
title = "Exact relations for effective tensors of polycrystals.
{I}{I}. {A}pplications to elasticity and
piezoelectricity",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "143",
number = "4",
pages = "331--356",
year = "1998",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Grabovsky:1998:EREa,
author = "Y. Grabovsky",
title = "Exact relations for effective tensors of polycrystals.
{I}. Necessary conditions",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "143",
number = "4",
pages = "309--329",
year = "1998",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Grabovsky:1998:ROP,
author = "Y. Grabovsky and G. W. Milton",
fullauthor = "Yury Grabovsky and G. W. Milton",
title = "Rank one plus a null-{Lagrangian} is an inherited
property of two-dimensional compliance tensors under
homogenization",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "128",
number = "2",
pages = "283--299",
year = "1998",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
xxjournal = "Proc. Roy. Soc. Edinburgh Sect. A",
xxtitle = "Rank one plus a null-{Lagrangian} is an inherited
property of two-dimensional compliance tensors under
homogenisation",
}
@Article{Grabovsky:1999:ERE,
author = "Y. Grabovsky and G. W. Milton and D. S. Sage",
title = "Exact relations for effective tensors of polycrystals:
Necessary conditions and sufficient conditions",
journal = "in preparation",
year = "1999",
}
@Book{Green:1992:TE,
author = "A. E. Green and W. Zerna",
title = "Theoretical elasticity",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "second",
pages = "xvi + 457",
year = "1992",
ISBN = "0-486-67076-7",
}
@InCollection{Greengard:1997:NVF,
author = "L. Greengard and V. Rokhlin",
booktitle = "Acta numerica, 1997",
title = "A new version of the fast multipole method for the
Laplace equation in three dimensions",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "229--269",
year = "1997",
}
@Article{Greengard:1998:NEE,
author = "L. Greengard and J. Helsing",
title = "On the numerical evaluation of elastostatic fields in
locally isotropic two-dimensional composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "46",
number = "8",
pages = "1441--1462",
year = "1998",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Book{Grinfeld:1991:TMT,
author = "M. A. Grinfeld",
title = "Thermodynamic methods in the theory of heterogeneous
systems",
publisher = "Longman",
address = "New York",
year = "1991",
}
@Article{Guedes:1996:PMP,
author = "J. M. Guedes and J. E. Taylor",
title = "On the prediction of material properties and topology
for optimal continuum structures",
journal = j-STRUCT-OPTIM,
volume = "14",
pages = "193--199",
year = "1996",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@InCollection{Gurtin:1972:LTE,
author = "M. E. Gurtin",
booktitle = "Handbuch der Physik",
title = "The linear theory of elasticity",
volume = "6a/2",
publisher = pub-SV,
address = "New York",
pages = "1--295",
year = "1972",
}
@InProceedings{Haber:1994:VTS,
author = "R. B. Haber and C. Jog and M. P. Bend\-s{\o}e",
editor = "B. Gilmore and others",
booktitle = "Advances in Design Automation",
title = "Variable-topology shape optimization with a constraint
on perimeter",
volume = "DE 69-2",
publisher = "ASME",
address = "New York",
pages = "261--272",
year = "1994",
}
@Article{Haber:1996:NAV,
author = "R. B. Haber and C. Jog and M. P. Bend\-s{\o}e",
title = "A New Approach to Variable-Topology Shape Design Using
a Constraint on Perimeter",
journal = j-STRUCT-OPTIM,
volume = "11",
number = "",
pages = "1--12",
year = "1996",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@InCollection{Haber:1996:PCT,
author = "R. B. Haber and M. P. Bend\-s{\o}e and C. Jog",
booktitle = "IUTAM Symposium on Optimization of Mechanical Systems
(Stuttgart, 1995)",
title = "Perimeter constrained topology optimization of
continuum structures",
publisher = pub-KLUWER,
address = "Dordrecht",
pages = "113--120",
year = "1996",
}
@Article{Haftka:1986:SSO,
author = "R. T. Haftka and R. V. Gandhi",
title = "Structural Shape Optimization - {A} Survey",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "57",
number = "",
pages = "91--106",
year = "1986",
CODEN = "CMMECC",
ISSN = "0045-7825",
}
@Book{Haftka:1992:ESO,
author = "R. T. Haftka and Z. G{\"u}rdal",
title = "Elements of structural optimization",
publisher = pub-KLUWER,
address = "Dordrecht",
edition = "Third",
pages = "xiv + 481",
year = "1992",
ISBN = "0-7923-1504-9",
MRnumber = "MR92m:73088",
}
@Article{Halperin:1985:DBL,
author = "B. I. Halperin and S. Feng and P. N. Sen",
title = "Differences between lattice and continuum percolation
transport exponents",
journal = j-PHYS-REV-LET,
volume = "54",
pages = "2391--2394",
year = "1985",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Hamburger:1987:CRO,
author = "C. Hamburger",
title = "A characterization for rank-one-convexity in two
dimensions",
journal = j-RIC-MAT,
volume = "36",
number = "2",
pages = "171--181",
year = "1987",
CODEN = "RCMTAE",
ISSN = "0035-5038",
fjournal = "Ricerche di Matematica",
}
@Book{Hanyga:1985:MTNa,
author = "A. Hanyga",
title = "Mathematical theory of nonlinear elasticity",
publisher = pub-EH,
address = pub-EH:adr,
pages = "432",
year = "1985",
ISBN = "0-85312-227-X",
note = "Translated from the Polish, Translation edited by R.
W. Ogden.",
}
@Book{Hanyga:1985:MTNb,
author = "A. Hanyga",
title = "Mathematical theory of nonlinear elasticity",
publisher = "PWN---Polish Scientific Publishers",
address = "Warsaw",
pages = "432",
year = "1985",
ISBN = "83-01-04722-4",
note = "Translated from the Polish, Translation edited by R.
W. Ogden.",
}
@Article{Haraux:1985:ISP,
author = "A. Haraux and F. Murat",
title = "Influence of a singular perturbation on the infimum of
some functionals",
journal = j-J-DIFFER-EQU,
volume = "58",
number = "1",
pages = "43--75",
year = "1985",
CODEN = "JDEQAK",
ISSN = "0022-0396",
fjournal = "Journal of Differential Equations",
}
@Book{Hardy:1988:I,
author = "G. H. Hardy and J. E. Littlewood and G. P{\'o}lya",
title = "Inequalities",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "xii + 324",
year = "1988",
ISBN = "0-521-35880-9",
}
@Article{Harris:1977:CBR,
author = "A. B. Harris and R. Fisch",
title = "Critical behavior of random resistor networks",
journal = j-PHYS-REV-LET,
volume = "38",
pages = "796--799",
year = "1977",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Hashin:1962:EMH,
author = "Z. Hashin",
title = "The elastic moduli of heterogeneous materials",
journal = j-J-APPL-MECH,
volume = "29",
pages = "143--150",
year = "1962",
CODEN = "JAMCAV",
ISSN = "0021-8936",
MRnumber = "MR24:B2161",
xxjournal = "ASME J. Applied Mech.",
}
@Article{Hashin:1962:VATa,
author = "Z. Hashin and S. Shtrikman",
title = "A variational approach to the theory of the effective
magnetic permeability of multiphase materials",
journal = j-J-APPL-PHYS,
volume = "35",
pages = "3125--3131",
year = "1962",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Hashin:1962:VATb,
author = "Z. Hashin and S. Shtrikman",
title = "A variational approach to the theory of the elastic
behavior of polycrystals",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "10",
pages = "343--352",
year = "1962",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Hashin:1963:VAT,
author = "Z. Hashin and S. Shtrikman",
title = "A variational approach to the theory of the elastic
behavior of multiphase materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "11",
pages = "127--140",
year = "1963",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@InCollection{Hashin:1964:BVC,
author = "Z. Hashin",
booktitle = "Second-order Effects in Elasticity, Plasticity and
Fluid Dynamics (Internat. Sympos., Haifa, 1962)",
title = "Bounds for viscosity coefficients of fluid mixtures by
variational methods",
publisher = "Jerusalem Academic Press",
address = "Jerusalem",
pages = "434--449",
year = "1964",
MRnumber = "MR29:3094",
}
@Article{Hashin:1965:EBF,
author = "Z. Hashin",
title = "On elastic behaviour of fibre reinforced materials of
arbitrary transverse phase geometry",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "13",
pages = "119--134",
year = "1965",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Hashin:1970:CMVa,
author = "Z. Hashin",
title = "Complex moduli of an viscoelastic composites: {I}
General theory and application to particulate
composites",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "6",
pages = "539--552",
year = "1970",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Hashin:1970:CMVb,
author = "Z. Hashin",
title = "Complex moduli of an viscoelastic composites: {II}
Fiber reinforced materials,",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "6",
pages = "797--807",
year = "1970",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@InCollection{Hashin:1970:TCM,
author = "Z. Hashin",
editor = "F. W. Wendt and U. Liebowitz and N. Perrone",
booktitle = "Mechanics of composite materials",
title = "Theory of composite materials",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "257--282",
year = "1970",
}
@TechReport{Hashin:1970:TFR,
author = "Z. Hashin",
title = "Theory of fiber reinforced materials",
type = "Report",
number = "Contract NAS1-8818",
institution = "University of Pennsylvania",
address = "Phyladelpia, PA",
year = "1970",
}
@Article{Hashin:1983:ACM,
author = "Z. Hashin",
title = "Analysis of composite materials: a survey",
journal = j-J-APPL-MECH,
volume = "50",
pages = "481--505",
year = "1983",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@Article{Hashin:1988:DSA,
author = "Z. Hashin",
title = "The differential scheme and its application to cracked
materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "36",
number = "6",
pages = "719--734",
year = "1988",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR90c:73103",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Hashin:1991:TPP,
author = "Z. Hashin",
title = "Thermoelastic properties of particulate composites
with imperfect interface",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "39",
number = "6",
pages = "745--762",
year = "1991",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR92g:73013",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Hashin:1992:EPE,
author = "Z. Hashin",
title = "Extremum principles for elastic heterogenous media
with imperfect interfaces and their application to
bounding of effective moduli",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "40",
number = "4",
pages = "767--781",
year = "1992",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR93b:73006",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Hashin:1993:CTP,
author = "Z. Hashin",
title = "Corrigendum: ``{Thermoelastic} properties of
particulate composites with imperfect interface'' [{J}.
{Mech}.\ {Phys}.\ {Solids} {\bf 39} (1991), no.\ 6,
745--762; {MR} 92g:73013]",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "41",
number = "9",
pages = "1571",
year = "1993",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR1234143",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Haslinger:1995:OCM,
author = "J. Haslinger and J. Dvo{\v{r}}{\'a}k",
title = "Optimum Composite Material Design",
journal = j-MATH-MODEL-NUM-ANA,
year = "1995",
CODEN = "RMMAEV",
ISSN = "0764-583X",
abstract = "For a scalar elliptic linear PDE (the steady heat
transfer equation), we consider the problem of
numerical microstructure identification: Given certain
two phases and a certain matrix of coefficients, what
is the microstructure in which the phases are to be
mixed so that the effective coefficient matrix of the
resulting composite is the closest to the prescribed
target matrix? We look for solutions in the class of
single inclusion microgeometries. Using the numerical
tool for microstructure identification, we study the
extremal microstructures --- those that
maximize/minimize the effective internal energy subject
to a constraint on the volume fraction of the phases
--- we attempt to identify the boundaries of the
$G_\theta$ sets numerically. The article contains
illustrative figures",
keywords = "homogenization, microstructure identification,
extremal microstructures, optimum shape design",
}
@Article{Haug:1980:DSAa,
author = "E. J. Haug and B. Rousselet",
title = "Design Sensitivity Analysis in Structural Mechanics
{I}",
journal = j-J-STRUCT-MECH,
volume = "8",
number = "1",
pages = "17--41",
year = "1980",
CODEN = "JSMHA2",
ISSN = "0360-1218",
}
@Article{Haug:1980:DSAb,
author = "E. J. Haug and B. Rousselet",
title = "Design Sensitivity Analysis in Structural Mechanics
{II}",
journal = j-J-STRUCT-MECH,
volume = "8",
number = "2",
pages = "161--186",
year = "1980",
CODEN = "JSMHA2",
ISSN = "0360-1218",
}
@Book{Haug:1986:DSA,
author = "E. J. Haug and K. K. Choi and V. Komkov",
title = "Design Sensitivity Analysis of Structural System",
publisher = pub-AP,
address = pub-AP:adr,
pages = "",
year = "1986",
series = "Mathematics in Science and Engineering. Volume 177",
}
@Article{Helsing:1991:ECA,
author = "J. Helsing and A. Helte",
title = "Effective conductivity of aggregates of anisotropic
grains",
journal = j-J-APPL-PHYS,
volume = "69",
pages = "3583",
year = "1991",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Helsing:1997:DRC,
author = "J. Helsing and G. W. Milton and A. B. Movchan",
title = "Duality relations, correspondences and numerical
results for planar elastic composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "4",
pages = "565--590",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Book{Hemp:1973:OS,
author = "W. Hemp",
title = "Optimum structures",
publisher = "Calderon press",
year = "1973",
}
@Article{Hill:1952:EBC,
author = "R. Hill",
title = "The elastic behavior of a crystalline aggregate",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "65",
pages = "349--354",
year = "1952",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@Article{Hill:1961:UGB,
author = "R. Hill",
title = "Uniqueness in general boundary-value problems for
elastic or inelastic solids",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "9",
pages = "114--130",
year = "1961",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR22:8793",
}
@Article{Hill:1963:EPR,
author = "R. Hill",
title = "Elastic properties of reinforced solids: {Some}
theoretical principles",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "11",
pages = "357--372",
year = "1963",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@InCollection{Hill:1963:NDS,
author = "R. Hill",
booktitle = "Progress in Applied Mechanics",
title = "New derivations of some elastic extremum principles",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
pages = "99--106",
year = "1963",
MRnumber = "MR28:3572",
}
@Article{Hill:1964:TMP,
author = "R. Hill",
title = "Theory of mechanical properties of fibre-strengthened
materials. {I}. {Elastic} behaviour",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "12",
pages = "199--212",
year = "1964",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Hill:1972:ITI,
author = "R. Hill",
booktitle = "Continuum mechanics and related problems of analysis
(on the occasion of the eightieth birthday of
Academician N. I. Musheli\v svili) (Russian)",
title = "An invariant treatment of interfacial discontinuities
in elastic composites",
publisher = "Izdat. ``Nauka'', Moscow",
pages = "597--604",
year = "1972",
MRnumber = "MR51:14720",
}
@Article{Hong:1986:RWA,
author = "D. C. Hong and H. E. Stanley and A. Coniglio and A.
Bunde",
title = "Random Walk approach to the two-component
random-conductor mixture: Perturbing away from the
perfect random resistor network and random
superconducting-network limits",
journal = j-PHYS-REV-B,
volume = "33",
pages = "4564--4573",
year = "1986",
CODEN = "PLRBAQ",
ISSN = "0556-2805",
}
@InProceedings{Hornung:1987:MCR,
author = "U. Hornung and W. J{\"a}ger",
editor = "J. Warnatz and W. J{\"a}ger",
booktitle = "Complex Chemical Reaction Systems. Mathematical
Modeling and Simulation",
title = "A Model for Chemical Reactions in Porous Media",
publisher = pub-SV,
address = "Berlin",
pages = "318--334",
year = "1987",
}
@Article{Hornung:1990:DDP,
author = "U. Hornung and T. Arbogast and J. {Douglas, Jr.}",
title = "Derivation of the Double Porosity Model of Single
Phase Flow via Homogenization Theory",
journal = j-SIAM-J-MATH-ANA,
volume = "21",
pages = "823--836",
year = "1990",
CODEN = "SJMAAH",
ISSN = "0036-1410",
}
@Article{Hornung:1990:DMF,
author = "U. Hornung and R. Showalter",
fullauthor = "U. Hornung and Ralph Showalter",
title = "Diffusion Models for Fractured Media",
journal = j-J-MATH-ANAL-APPL,
volume = "147",
pages = "69--80",
year = "1990",
CODEN = "JMANAK",
ISSN = "0022-247X",
}
@Article{Hornung:1991:DCA,
author = "U. Hornung and W. J{\"a}ger",
title = "Diffusion, Convection, Adsorption, and Reaction of
Chemicals in Porous Media",
journal = j-J-DIFFER-EQU,
volume = "92",
pages = "199--225",
year = "1991",
CODEN = "JDEQAK",
ISSN = "0022-0396",
}
@InProceedings{Hornung:1991:HMD,
author = "U. Hornung",
editor = "G. {Dal Maso} and G. F. Dell'Antonio",
booktitle = "Composite Media and Homogenization Theory, ICTP,
Trieste 1990",
title = "Homogenization of Miscible Displacement in Unsaturated
Aggregated Soils",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "143--153",
year = "1991",
series = "Progress in Nonlinear Differential Equations and Their
Applications",
}
@Article{Hornung:1991:MDP,
author = "U. Hornung",
title = "Miscible displacement in porous media influenced by
mobile and immobile water",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "21.2",
pages = "645--669, corr. 1153--1158",
year = "1991",
CODEN = "RMJMAE",
ISSN = "0035-7596",
}
@InProceedings{Hornung:1991:MNF,
author = "U. Hornung and T. Arbogast and J. {Douglas, Jr.}",
fullauthor = "U. Hornung and Todd Arbogast and Jim {Douglas, Jr.}",
editor = "Dautray R.",
booktitle = "Frontiers in Pure and Applied Mathematics",
title = "Modeling of Naturally Fractured Petroleum Reservoirs
by Formal Homogenization Techniques",
publisher = "Elsevier, Amsterdam",
pages = "1--19",
year = "1991",
}
@InProceedings{Hornung:1992:AHM,
author = "U. Hornung",
editor = "Xiao Shutie",
booktitle = "Summer School on Flow and Transport in Porous Media",
title = "Applications of the homogenization method to flow and
transport in porous media",
publisher = pub-WORLD-SCI,
address = "Singapore",
pages = "167--222",
year = "1992",
}
@Article{Hornung:1992:MSA,
author = "U. Hornung",
title = "{Modellierung von Stofftransport in aggregierten und
gekl{\"u}fteten B{\"o}den}",
journal = j-WASSERWIRTSCHAFT,
volume = "92.1",
year = "1992",
CODEN = "WSWTAR",
ISSN = "0043-0978",
}
@InProceedings{Hornung:1993:HRT,
author = "U. Hornung and W. J{\"a}ger",
editor = "Perell{\'o} C. and Sim{\'o} C. and Sol{\`a}-Morales
J",
booktitle = "International Conference on Differential Equations,
Barcelona 1991",
title = "Homogenization of Reactive Transport through Porous
Media",
publisher = pub-WORLD-SCI,
address = "Singapore",
pages = "136--152",
year = "1993",
}
@TechReport{Hornung:1993:MFT,
author = "U. Hornung",
title = "Models for Flow and Transport through Porous Media
Derived by Homogenization",
type = "Preprint",
number = "1148",
institution = "IMA",
address = "Minneapolis, Minnesota",
year = "1993",
}
@Article{Hornung:1994:RTT,
author = "U. Hornung and W. J{\"a}ger and Andro Mikeli{\'c}",
title = "Reactive Transport through an Array of Cells with
Semipermeable Membranes",
journal = j-MATH-MODEL-NUM-ANA,
volume = "28",
number = "1",
pages = "59--94",
year = "1994",
CODEN = "RMMAEV",
ISSN = "0764-583X",
}
@Book{Hornung:1997:HPM,
editor = "U. Hornung",
fulleditor = "Ulrich Hornung",
title = "Homogenization and porous media",
publisher = pub-SV,
address = "New York",
pages = "xvi + 275",
year = "1997",
ISBN = "0-387-94786-8",
}
@InProceedings{Hornung:19xx:MFT,
author = "U. Hornung",
editor = "M. F. Wheeler",
booktitle = "Environmental Studies: Mathematical, Computational,
and Statistical Analysis",
title = "Models for Flow and Transport through Porous Media
Derived by Homogenization",
publisher = pub-SV,
address = "New York",
year = "19xx",
note = "To appear.",
series = "IMA Volumes on Mathematics",
}
@Article{Hutchinson:1972:DVM,
author = "John W. Hutchinson and Frithiof I. Niordson",
booktitle = "Continuum mechanics and related problems of analysis
(on the occasion of the eightieth birthday of
Academician N. I. Musheli\v svili) (Russian)",
title = "Designing vibrating membranes",
publisher = "Izdat. ``Nauka''",
address = "Moscow",
pages = "581--590",
year = "1972",
}
@Book{Ioffe:1979:TEP,
author = "A. D. Ioffe and V. M. Tihomirov",
title = "Theory of extremal problems",
publisher = pub-NH,
address = pub-NH:adr,
pages = "xii + 460",
year = "1979",
ISBN = "0-444-85167-4",
note = "Translated from the Russian by Karol Makowski",
}
@Book{Jacobson:1968:SRJ,
author = "N. Jacobson",
title = "Structure and representations of {Jordan} algebras",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "x + 453",
year = "1968",
note = "American Mathematical Society Colloquium Publications,
Vol. XXXIX.",
}
@TechReport{Jager:1993:APL,
author = "W. {J{\"a}ger } and O. A. Ole{\u\i}nik and A. S.
Schamajev",
title = "Averaging Problem for {Laplace} Equation in a
Partially Perforated Domain (in {Russian})",
number = "333/4",
institution = "Dokladi Akademii Nauk (DAN) (Papers of the Academy of
Sciences)",
year = "1993",
}
@TechReport{Jager:1993:HLE,
author = "W. {J{\"a}ger } and Andro Mikeli{\'c}",
title = "Homogenization of the {Laplace} Equation in a
Partially Perforated Domain",
number = "157",
institution = "Equipe d'Analyse Num{\'e}rique Lyon Saint-Etienne,
C.N.R.S. U.R.A. 740",
year = "1993",
abstract = "We consider the {Laplace} equation in a bounded domain
consisting of a porous medium, a nonperforated domain
and an interface between them. The homogeneous
Dirichlet's condition is prescribed on the boundaries
of the perforations. We suppose the porous medium
having a periodic structure with a period $\epsilon$
and consider the limit $\epsilon \longrightarrow 0$.
The effective behaviors inside the porous medium and
the nonperforated domain are obtained and in addition
the boundary conditions to be imposed at the interface
between two media are determined. Using the boundary
layers describing interaction between two very
different media we estimate the $L^2$-norm of the
difference between the solution $u^\epsilon$ of the
$\epsilon$-problem and the effective behavior terms and
show that it is bounded from above by
$C\epsilon^{\frac{1}{2}}$. Finally, we calculate the
weak $L^2$-limit of the renormalized function
$\frac{u^\epsilon}{\epsilon^2}$ and weak
$M(\Omega)$-limit of the renormalized $\nabla
\frac{u^\epsilon} {\epsilon^2}$.",
}
@TechReport{Jager:1993:HPL,
author = "W. {J{\"a}ger } and O. A. Ole{\u\i}nik and A. S.
Schamajev",
title = "On a homogenization problem for the {Laplace} operator
in a partially perforated domain with the {Neumann}
condition on holes",
number = "93--53",
institution = "Interdisziplin{\"a}res Zentrum fuer Wissenschaftliches
Rechnen",
year = "1993",
}
@TechReport{Jager:1994:BCC,
author = "W. J{\"a}ger and Andro Mikeli{\'c}",
title = "On the Boundary Conditions at the Contact Interface
between a Porous Medium and a Free Fluid",
number = "94--58",
institution = "Interdisziplin{\"a}res Zentrum f{\"u}r
Wissenschaftliches Rechnen",
address = "Universit{\"a}t Heidelberg",
year = "1994",
abstract = "We consider a slow viscous flow in a two-dimensional
domain consisting of a porous medium and a free fluid
domain. At the boundaries of the solid part of porous
medium we suppose the no-slip boundary condition.
Supposing a periodic porous medium with period
proportional to the characteristic pore size and a
fixed porosity and using the homogenization, we find
conditions on the interface linking pressures and
velocities. Furthermore, we estimate the $L^2$-norm of
the difference between the solution for some pores size
$\varepsilon $ and the combination of solutions of the
limit problems and show the convergence as
$\varepsilon$ tends to zero. We distinguish (a) the
balanced flow in free fluid domain and in porous medium
and (b) the small flow in porous medium caused by the
flow in free fluid domain. In the case (a) we obtain
continuity of the normal velocities at the interface
and the value of Darcy's pressure at the interface is
equal to zero. In (b) at the interface difference
between the Darcy pressure and the pressure of free
fluid is proportional to the tangential component of
the viscous stress corresponding to the free fluid. The
free fluid flow is behaving as an uncoupled {Stokes}
flow with no slip condition for the velocity at the
interface.",
}
@Article{Jarusek:1992:VIV,
author = "J. Jaru{\v{s}}ek and J. M{\'a}lek and J. Ne{\v{c}}as
and V. {\v{S}}ver{\'a}k",
title = "Variational inequality for a viscous drum vibrating in
the presence of an obstacle",
journal = j-REND-MAT-APPL-1981,
volume = "12",
number = "4",
pages = "943--958",
year = "1992",
CODEN = "RNMTAN",
ISSN = "1120-7183",
fjournal = "Rendiconti di Matematica e delle sue Applicazioni.
Serie VII",
xxyear = "1993",
}
@Book{Jikov:1994:HDO,
author = "V. V. Jikov and S. M. Kozlov and O. A. Ole{\u\i}nik",
title = "Homogenization of differential operators and integral
functionals",
publisher = pub-SV,
address = "Berlin",
pages = "xii + 570",
year = "1994",
ISBN = "3-540-54809-2",
note = "Translated from the Russian by G. A. Yosifian [G. A.
Iosif\cprime yan].",
}
@InProceedings{Jog:1992:DBT,
author = "C. Jog and R. B. Haber and M. P. Bend\-s{\o}e",
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "Topology Design of Structures",
title = "A displacement based topology design with
self-adaptive materials",
publisher = pub-KLUWER,
address = "Amsterdam",
pages = "219--238",
year = "1992",
}
@InProceedings{Jog:1993:DBT,
author = "C. Jog and R. B. Haber and M. P. Bend\-s{\o}e",
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "Topology Design of Structures, {Sesimbra, Portugal}",
title = "A Displacement-Based Topology Design Method with
Self-Adaptive Layered Materials",
organization = "NATO ASI",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "219--243",
month = "",
year = "1993",
}
@Article{Jog:1994:TDO,
author = "C. Jog and R. B. Haber and M. P. Bend\-s{\o}e",
title = "Topology Design with Optimized Self-Adaptive
Materials",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "8",
pages = "1323--1350",
year = "1994",
CODEN = "IJNMBH",
ISSN = "0029-5981",
fjournal = "International Journal for Numerical Methods in
Engineering",
}
@Article{Jog:1996:SFE,
author = "C. Jog and R. B. Haber",
title = "Stability of Finite Element Models for
Distributed-Parameter Optimization and Topology
Design",
journal = "Journal for Computational Methods in Applied Mechanics
and Engineering",
volume = "130",
number = "8",
pages = "203--226",
year = "1996",
}
@InProceedings{Junichi:1991:ACB,
author = "F. Junichi and K. Suzuki and N. Kikuchi",
editor = "G. I. N. Rozwany",
booktitle = "Optimization of Large Structural Systems",
title = "Applications to Car Bodies: Generalized Layout Design
of Three-Dimensional Shells for Car Bodies",
organization = "NATO ASI",
publisher = "Lecture Notes",
address = "Berchtesgarden Garden, Germany",
pages = "127--138",
month = "",
year = "1991",
}
@Article{Jurak:19xx:HCO,
author = "M. Jurak",
title = "Homogenization of Capillary Oscillations of an
Inviscid Fluid in a Porous Reservoir",
journal = j-BOLL-UNIONE-MAT-ITAL,
year = "19xx",
CODEN = "BLUMAM",
ISSN = "0041-7084",
abstract = "We consider small gravitational oscillations of an
ideal fluid in a cylindrical reservoir. Besides
gravity, surface tension at the free boundary is
considered. The reservoir contains a large number of
vertical solid tubes, periodically distributed over the
reservoir's cross section. Taking the period $\epsilon$
of the structure as parameter we get a sequence of
generalized eigenproblems. We find the limit problem
when the period $\epsilon$ tends to zero. Furthermore,
we show convergence of the eigenvalues and the
eigenspaces of the hydrodynamical problems towards that
of the limit problem. In the proof we use a
modification of theorem due to Yosifian, Oleinik and
Shamaev [Uspechi. Mat. Nauk. 44 (1989), 157-158]",
}
@InCollection{Kacimi:1989:EEP,
author = "H. Kacimi and F. Murat",
fullauthor = "Hayat Kacimi and F. Murat",
booktitle = "Partial differential equations and the calculus of
variations, Vol.\ II",
title = "Estimation de l'erreur dans des probl{\`e}mes de
{Dirichlet} o{\`u} apparait un terme \'etrange",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "661--696",
year = "1989",
}
@Article{Kaganova:1987:ESI,
author = "I. Kaganova and A. Roitburd",
title = "Equilibrium shape of an inclusion in a solid",
journal = j-SOVIET-PHYS-DOKL,
volume = "32",
pages = "925--927",
year = "1987",
CODEN = "SPHDA9",
ISSN = "0038-5689",
}
@Article{Kantor:1984:IRB,
author = "Y. Kantor and D. J. Bergman",
title = "improved rigorous bounds on the effective elastic
moduli of a composite material",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "32",
pages = "41--62",
year = "1984",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Kardonski:1972:SCP,
author = "V. Kardonski and ?. Ro{\u{i}}tburd",
title = "On the shape of coherent precipitates",
journal = "Phys. Met. Metallurg. USSR",
volume = "33",
pages = "210--212",
year = "1972",
}
@Article{Karp:1962:EFB,
author = "S. N. Karp and F. C. Karal",
title = "The elastic-field behaviour in the neighbourhood of a
crack of arbitrary angle",
journal = j-COMM-PURE-APPL-MATH,
volume = "15",
number = "",
pages = "413--421",
year = "1962",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
}
@Article{Kawohl:1990:QRS,
author = "B. Kawohl and G. Sweers",
fullauthor = "Bernhard Kawohl and Guido Sweers",
title = "On quasiconvexity, rank-one convexity and symmetry",
journal = j-DELFT-PROG-REP,
volume = "14",
number = "4",
pages = "251--263",
year = "1990",
CODEN = "DPRFB3",
ISSN = "0304-985X",
fjournal = "Delft Progress Report",
}
@Article{Kawohl:1991:ANS,
author = "B. Kawohl and J. Stara and G. Wittum",
title = "Analysis and numerical studies of a problem of shape
design",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "114",
pages = "349--363",
year = "1991",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Keglevic:19xx:PPF,
author = "I. Keglevic",
title = "On the Plane Potential Flow Through the Inhomogeneous
Porous Line",
journal = j-Z-ANGE-MATH-MECH,
year = "19xx",
CODEN = "ZAMMAX",
ISSN = "0044-2267",
abstract = "The plane potential stationary flow of an inviscid
incompressible fluid through the porous straight line
or porous line segment is considered. On the porous
line the normal velocity is assumed to be linear
proportional to the pressure difference. With given
velocity at infinity, we have the formula of the
solution of the problem and the proof of the uniqueness
of the solution, except in the case, when the velocity
in the infinity is perpendicular to the porous line. In
this case we do not have any solutions",
}
@Article{Keller:1964:TCC,
author = "J. B. Keller",
title = "A theorem on the conductivity of a composite medium",
journal = j-J-MATH-PHYS,
volume = "5",
pages = "548--549",
year = "1964",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
}
@Article{Keller:1966:TC,
author = "Joseph B. Keller and Frithiof I. Niordson",
title = "The tallest column",
journal = j-J-MATH-MECH,
volume = "16",
pages = "433--446",
year = "1966",
CODEN = "JOMMAN",
ISSN = "0095-9057",
}
@Article{Khachaturyan:1969:TMP,
author = "A. G. Khachaturyan and G. A. Shatalov",
title = "Theory of macroscopic periodicity for a phase
transition in the solid state",
journal = j-SOV-PHYS-JETP,
volume = "29",
pages = "557--561",
year = "1969",
CODEN = "SPHJAR",
ISSN = "0038-5646",
}
@Book{Khachaturyan:1983:TST,
author = "A. G. Khachaturyan",
title = "Theory of structural transformation in solids",
publisher = pub-WILEY,
address = pub-WILEY:adr,
year = "1983",
}
@InCollection{Khruslov:1991:HMC,
author = "E. Ya. Khruslov",
booktitle = "Composite media and homogenization theory (Trieste,
1990)",
title = "Homogenized models of composite media",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "159--182",
year = "1991",
MRclass = "35B27 (73B27)",
MRnumber = "92m:35023",
bibdate = "Tue Mar 7 16:36:09 2000",
}
@InProceedings{Khruslov:1995:HMS,
author = "E. Ya. Khruslov",
booktitle = "Proceedings of the International Congress of
Mathematicians, Vol.\ 1, 2 (Z{\"u}rich, 1994)",
title = "Homogenized models of strongly inhomogeneous media",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "1270--1278",
year = "1995",
MRclass = "73B27 (35B27)",
MRnumber = "97i:73005",
MRreviewer = "David J. Bergman",
bibdate = "Tue Mar 7 16:36:06 2000",
}
@InProceedings{Kikuchi:1995:OST,
author = "N. Kikuchi and H. C. Cheng and Z. D. Ma",
booktitle = "Advances in Structural Optimization",
title = "Optimal Shape and Topology Design of Vibrating
Structures",
organization = "",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "189--222",
month = "",
year = "1995",
}
@InCollection{Kinderlehrer:1988:RAE,
author = "D. Kinderlehrer",
editor = "J. M. Ball",
booktitle = "Material instabilities in continuum mechanics
(Edinburgh, 1985--1986)",
title = "Remarks about equilibrium configurations of crystals",
publisher = "Oxford Univ. Press",
address = "New York",
pages = "217--241",
year = "1988",
series = "Oxford Sci. Publ.",
}
@Article{Kinderlehrer:1991:CYM,
author = "D. Kinderlehrer and P. Pedregal",
title = "Characterizations of {Young} measures generated by
gradients",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "115",
number = "4",
pages = "329--365",
year = "1991",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Book{Kinderlehrer:1993:MPT,
editor = "D. Kinderlehrer and R. James and M. Luskin and J. L.
Ericksen",
title = "Microstructure and phase transition",
publisher = pub-SV,
address = "New York",
pages = "xvi + 215",
year = "1993",
ISBN = "0-387-94112-6",
MRnumber = "MR95i:73004",
}
@Article{Kinderlehrer:1994:GYM,
author = "D. Kinderlehrer and P. Pedregal",
title = "Gradient {Young} measures generated by sequences in
{Sobolev} spaces",
journal = j-J-GEOM-ANAL,
volume = "4",
number = "1",
pages = "59--90",
year = "1994",
CODEN = "JGANEG",
ISSN = "1050-6926",
fjournal = "The Journal of Geometric Analysis",
}
@Article{Kinoshita:1971:EFI,
author = "N. Kinoshita and T. Mura",
title = "Elastic fields of inclusions in anisotropic media",
journal = j-PHYS-STATUS-SOLIDI,
volume = "5",
pages = "759--768",
year = "1971",
ISSN = "0031-8957",
}
@Article{Klosowicz:1971:ONT,
author = "B. Klosowicz and K. A. Lurie",
title = "On the optimal nonhomogeneity of a torsional elastic
bar",
journal = j-ARCH-MECH,
volume = "24",
number = "2",
pages = "239--249",
year = "1971",
CODEN = "AVMHBR",
ISSN = "0373-2029",
bibdate = "Tue Mar 7 16:37:32 2000",
}
@Article{Klosowicz:1972:ONT,
author = "B. K{\l}osowicz and K. A. {\L}urie",
title = "On the optimal nonhomogeneity of a torsional elastic
bar",
journal = "Arch. Mech. (Arch. Mech. Stos.)",
volume = "24",
pages = "239--249",
year = "1972",
}
@Article{Kloucek:1994:CDM,
author = "P. Klou{\v{c}}ek and M. Luskin",
title = "The computation of the dynamics of the martensitic
transformation",
journal = j-CONTIN-MECH-THERMODYN,
volume = "6",
number = "3",
pages = "209--240",
year = "1994",
CODEN = "CMETEJ",
ISSN = "0935-1175",
MRnumber = "MR95d:73009",
fjournal = "Continuum Mechanics and Thermodynamics. Models and
Analysis of Complex Materials",
}
@Article{Kloucek:1994:CMM,
author = "P. Klou{\v{c}}ek and M. Luskin",
title = "Computational modeling of the martensitic
transformation with surface energy",
journal = j-MATH-COMP-MODELLING,
volume = "20",
number = "10-11",
pages = "101--121",
year = "1994",
CODEN = "MCMOEG",
ISSN = "0895-7177",
fjournal = "Mathematical and Computer Modelling",
}
@InProceedings{Kohler:1982:BEC,
author = "W. Kohler and G. C. Papanicolaou",
editor = "R. Burridge and S. Childress and G. Papanicolaou",
booktitle = "Macroscopic properties of disordered media",
title = "Bounds for effective conductivity of random media",
publisher = pub-SV,
address = pub-SV:adr,
pages = "111--130",
year = "1982",
}
@InCollection{Kohler:1997:LLF,
author = "W. Kohler and G. Papanicolaou and B. White",
booktitle = "Stochastic models in geosystems (Minneapolis, MN,
1994)",
title = "Localization of low frequency elastic waves",
publisher = pub-SV,
address = "New York",
pages = "209--217",
year = "1997",
MRnumber = "MR98k:73032",
}
@Article{Kohn:1983:ERV,
author = "R. V. Kohn and G. Strang",
title = "Explicit relaxation of a variational problem in
optimal design",
journal = j-BULL-AMS,
volume = "9",
pages = "211--214",
year = "1983",
CODEN = "BAMOAD",
ISSN = "0002-9904",
}
@InCollection{Kohn:1983:ODT,
author = "R. V. Kohn and G. Strang",
editor = "S. N. Alturi and R. H. Gallagher and O. C.
Zienkeiwicz",
booktitle = "Hybrid and mixed finite elements methods",
title = "Optimal design for torsional rigidity",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "281--288",
year = "1983",
}
@InCollection{Kohn:1983:SDO,
author = "R. V. Kohn and G. Strang",
editor = "R. Burridge and G. Papanicolaou and S. Childress",
booktitle = "Macroscopic Properties of Disordered Media",
title = "Structural design, optimization, homogenization, and
relaxation of variational problems",
volume = "154",
publisher = pub-SV,
pages = "??--??",
year = "1982",
series = "Lect. Notes Phys.",
}
@Article{Kohn:1985:NMT,
author = "R. V. Kohn and M. Vogelius",
title = "A new model for thin plates with rapidly varying
thickness. {II}. {A} convergence proof",
journal = j-QUART-APPL-MATH,
volume = "43",
number = "1",
pages = "1--22",
year = "1985",
CODEN = "QAMAAY",
ISSN = "0033-569X",
fjournal = "Quarterly of Applied Mathematics",
}
@InProceedings{Kohn:1986:BEC,
author = "R. V. Kohn and G. W. Milton",
editor = "J. Ericksen and others",
booktitle = "Homogenization and Effective Moduli of Materials and
Media (Minneapolis, Minn., 1984/1985)",
title = "On bounding the effective conductivity of anisotropic
composites",
publisher = pub-SV,
address = pub-SV:adr,
pages = "97--125",
year = "1986",
}
@Article{Kohn:1986:NMT,
author = "R. V. Kohn and M. Vogelius",
title = "A new model for thin plates with rapidly varying
thickness. {III}. {Comparison} of different scalings",
journal = j-QUART-APPL-MATH,
volume = "44",
number = "1",
pages = "35--48",
year = "1986",
CODEN = "QAMAAY",
ISSN = "0033-569X",
fjournal = "Quarterly of Applied Mathematics",
}
@Article{Kohn:1986:ODE,
author = "R. V. Kohn and G. Strang",
title = "Optimal Design in Elasticity and Plasticity",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "22",
number = "1",
pages = "183--188",
year = "1986",
CODEN = "IJNMBH",
ISSN = "0029-5981",
}
@Article{Kohn:1986:ODR,
author = "R. V. Kohn and G. Strang",
title = "Optimal design and relaxation of variational
problems",
journal = j-COMM-PURE-APPL-MATH,
volume = "39",
pages = "1--25 (part {I}), 139--182 (part {II}) and 353--357
(part {III})",
year = "1986",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
}
@Article{Kohn:1988:OBE,
author = "R. V. Kohn and R. Lipton",
title = "Optimal bounds for the effective energy of a mixture
of isotropic, incompressible, elastic materials",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "102",
number = "4",
pages = "331--350",
year = "1988",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Kohn:1991:RDW,
author = "R. V. Kohn",
title = "The relaxation of a double-well energy",
journal = j-CONTIN-MECH-THERMODYN,
volume = "3",
pages = "193--236",
year = "1991",
CODEN = "CMETEJ",
ISSN = "0935-1175",
}
@Article{Kohn:1992:BTN,
author = "R. V. Kohn and S. M{\"u}ller",
title = "Branching of twins near an
austenite/twinned-martensite interface",
journal = j-PHIL-MAGAZINE,
volume = "66A",
pages = "697--715",
year = "1992",
CODEN = "PHMAA4",
ISSN = "0031-8086",
}
@Article{Kohn:1994:SEM,
author = "R. V. Kohn and S. M{\"u}ller",
title = "Surface energy and microstructure in coherent phase
transitions",
journal = j-COMM-PURE-APPL-MATH,
volume = "47",
pages = "405--435",
year = "1994",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
}
@Article{Komorowski:1997:MGI,
author = "T. Komorowski and G. Papanicolaou",
title = "Motion in a {Gaussian} incompressible flow",
journal = j-ANN-APPL-PROBAB,
volume = "7",
number = "1",
pages = "229--264",
year = "1997",
ISSN = "1050-5164",
fjournal = "The Annals of Applied Probability",
}
@Article{Kozlov:1996:DED,
author = "S. M. Kozlov and A. L. Piatnitski",
title = "Degeneration of effective diffusion in the presence of
periodic potential",
journal = j-ANN-INST-HENRI-POINCARE-B,
volume = "32",
number = "5",
pages = "571--587",
year = "1996",
CODEN = "AHPBAR",
ISSN = "0246-0203",
fjournal = "Annales de l'Institut Henri Poincar\'e. Probabilit\'es
et Statistiques",
}
@Book{Krasnoselskii:1961:CFO,
author = "M. A. {Kras\-no\-sel{\cprime}\-ski{\u\i}} and Ja. B.
Ruticki{\u\i}",
title = "Convex functions and {Orlicz} spaces",
publisher = "P. Noordhoff Ltd.",
address = "Groningen",
pages = "xi + 249",
year = "1961",
note = "Translated from the first Russian edition by Leo F.
Boron",
}
@Book{Krasnov:1984:PEC,
author = "M. L. Krasnov and G. I. Makarenko and A. I. Kiselev",
title = "Problems and exercises in the calculus of variations",
publisher = "``Mir''",
address = "Moscow",
pages = "222",
year = "1984",
note = "Translated from the Russian by G. Yankovsky [G.
Yankovski\u\i ], Reprint of the 1975 translation.",
}
@Book{Krein:1977:MMP,
author = "M. G. Krein and A. A. Nudelman",
editor = "",
title = "The Markov Moment Problem and Extremal Problems",
volume = "",
publisher = pub-AMS,
address = pub-AMS:adr,
edition = "",
month = "",
year = "1977",
series = "Translation of Mathematical Monographs, 50",
}
@InProceedings{Krog:1995:TOI,
author = "L. A. Krog and N. Olhoff",
editor = "D. Bestle and W. Schiehlen",
booktitle = "Optimization of Mechanical Systems, {Stuttgart,
Germany}",
title = "Topology Optimization of Integral Rib Reinforcement of
Plate and Shell Structures with Weighted-Sum and
Max-Min Objectives.",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "171--179",
month = "",
year = "1995",
}
@InProceedings{Krog:1995:TOP,
author = "L. A. Krog and N. Olhoff",
editor = "N. Olhoff and G. I. N. Rozvany",
booktitle = "Structural and Multidisciplinary Optimization",
title = "Topology Optimization of Plate and Shell Structures
with Multiple Eigenfrequencies.",
organization = "",
publisher = "{Pergamon}, {Oxford}, {UK}, 1995",
address = "{Goslar}, {Germany}",
pages = "675--682",
month = "",
year = "1995",
}
@InProceedings{Krog:1997:TRL,
author = "L. A. Krog and N. Olhoff",
editor = "G. I. N. Rozvany",
booktitle = "Topology Optimization in Structural Mechanics",
title = "Topology and reinforcement layout optimization of
disk, plate, and shell structures",
organization = "CISM",
publisher = pub-SV,
address = pub-SV:adr,
pages = "237--322",
month = "",
year = "1997",
confaddress = "Udine, Italy",
}
@Article{Kunz:1978:ESP,
author = "H. Kunz and B. Souillard",
title = "Essential singularity in percolation problems and
asymptotic behavior of cluster size distribution",
journal = j-J-STAT-PHYS,
volume = "19",
pages = "77--106",
year = "1978",
CODEN = "JSTPSB",
ISSN = "0022-4715",
}
@Article{Kuttler:1982:BSE,
author = "J. R. Kuttler",
title = "Bounds for {Stekloff} eigenvalues",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "1",
pages = "121--125",
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
}
@Article{Lagache:1981:TVM,
author = "J.-M. Lagache",
title = "Treillis de volume minimal dans une region{\'e}
donn{\'e}e",
journal = j-J-MEC,
volume = "20",
pages = "415--448",
year = "1981",
CODEN = "JOMCAR",
ISSN = "0021-7832",
}
@Article{Lancaster:1962:EMD,
author = "P. Lancaster",
title = "On Eigenvalues of Matrices Dependent on a Parameter",
journal = j-NUM-MATH,
volume = "6",
number = "",
pages = "377--387",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X",
}
@Book{Landau:1984:ECM,
author = "L. D. Landau and E. M. Lifshitz",
title = "Electrodynamics of continuous media",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
year = "1984",
}
@Article{Larche:1994:SMC,
author = "F. C. Larch{\'e} and J. W. Cahn",
title = "A simple model for coherent equilibrium",
journal = j-ACTA-METALL-MATER,
volume = "32",
number = "11",
pages = "1915--1923",
year = "1994",
CODEN = "AMATEB",
ISSN = "0956-7151",
}
@Article{Larsen:1997:DFC,
author = "U. D. Larsen and O. Sigmund and S. Bouwstra",
title = "Design and fabrication of compliant mechanisms and
material structures with negative {P}oisson's ratio",
journal = "Journal of Microelectromechanical Systems",
volume = "6",
number = "2",
pages = "99--106",
month = jun,
year = "1997",
}
@Book{Lavrentev:1989:VMB,
author = "M. A. Lavrent{\cprime}ev",
title = "Variational methods for boundary value problems for
systems of elliptic equations",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "153",
year = "1989",
ISBN = "0-486-66170-9",
note = "Translated from the Russian by J. R. M. Radok",
}
@Article{Lavrov:1980:NHB,
author = "N. Lavrov and K. A. Lurie and A. V. Cherkaev",
title = "Non-Homogeneous Bar of Extremal Rigidity in Torsion (in
Russian)",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "6",
number = "",
pages = "",
year = "1980",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@Article{Laws:1973:TCM,
author = "N. Laws",
title = "On thermostatics of composite materials",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "21",
pages = "9--17",
year = "1973",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Lax:1983:SDLa,
author = "P. D. Lax and C. D. Levermore",
title = "The small dispersion limit of the {Korteweg de Vries}
equation. {I}",
journal = j-COMM-PURE-APPL-MATH,
volume = "36",
number = "3",
pages = "253--290",
year = "1983",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
MRnumber = "MR85g:35105a",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Lax:1983:SDLb,
author = "P. D. Lax and C. D. Levermore",
title = "The small dispersion limit of the {Korteweg de Vries}
equation. {II}",
journal = j-COMM-PURE-APPL-MATH,
volume = "36",
number = "5",
pages = "571--593",
year = "1983",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
MRnumber = "MR85g:35105b",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Lax:1983:SDLc,
author = "P. D. Lax and C. D. Levermore",
title = "The small dispersion limit of the {Korteweg de Vries}
equation. {III}",
journal = j-COMM-PURE-APPL-MATH,
volume = "36",
number = "6",
pages = "809--829",
year = "1983",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Lee:1952:STEa,
author = "T. D. Lee and C. N. Yang",
title = "Statistical theory of equations of state and phase
transitions. {I}. Theory of condensation",
journal = j-PHYS-REV,
volume = "87",
pages = "404--409",
year = "1952",
CODEN = "PHRVAO",
ISSN = "0031-899X",
}
@Article{Lee:1952:STEb,
author = "T. D. Lee and C. N. Yang",
title = "Statistical theory of equations of state and phase
transitions. {II}. Lattice gas and {Ising} model",
journal = j-PHYS-REV,
volume = "87",
pages = "410--419",
year = "1952",
CODEN = "PHRVAO",
ISSN = "0031-899X",
}
@Article{Lee:1977:ESE,
author = "J. K. Lee and D. M. Barnett and H. I. Aaronson",
title = "The elastic strain energy of coherent ellipsoidal
precipitates in anisotropic crystalline solids",
journal = j-METALL-TRANS-A-PHYS-METALL-MATER-SCI,
volume = "8A",
pages = "963--970",
year = "1977",
CODEN = "MTTABN",
ISSN = "0360-2133",
}
@Book{Leitmann:1981:CVO,
author = "G. Leitmann",
title = "The calculus of variations and optimal control",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "xvi + 311",
year = "1981",
ISBN = "0-306-40707-8",
note = "An introduction, Posebna Izdanja [Special Editions],
14.",
}
@Book{Lekhnitskii:1981:TEA,
author = "S. G. Lekhnitski{\u\i}",
title = "Theory of elasticity of an anisotropic body",
publisher = "``Mir''",
address = "Moscow",
edition = "Russian",
pages = "431",
year = "1981",
}
@Article{Leonetti:1997:QSC,
author = "F. Leonetti and V. Nesi",
title = "Quasiconformal solutions to certain first order
systems and the proof of a conjecture of {G}. {W}.
{Milton}",
journal = j-J-MATH-PURES-APPL,
volume = "76",
number = "2",
pages = "109--124",
year = "1997",
CODEN = "JMPAAM",
ISSN = "0021-7824",
fjournal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es.
Neuvi{\'e}me S{\'e}rie",
}
@Article{Levin:1967:TEC,
author = "V. M. Levin",
title = "Thermal expansion coefficients of heterogeneous
materials",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "2",
number = "1",
pages = "88--94",
year = "1967",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@InCollection{Levin:1999:EWP,
author = "V. M. Levin",
editor = "K. Markov and E. Inan",
booktitle = "Continuum models and discrete systems",
title = "The elastic wave propagation in the piezoelectric
fiber reinforced composites",
publisher = "World Scientific Publishing Co. Inc.",
address = "River Edge, NJ",
year = "1999",
}
@TechReport{Levy:1994:ANL,
author = "T. L{\'e}vy",
title = "Acoustique non lin{\'e}aire en milieu poreux rigide",
type = "1994",
number = "319",
institution = "C. R. Acad. Sci. Paris",
address = "Paris",
year = "1994",
note = "isotropy.",
abstract = "The homogenization method for periodic media is used
in order to study the influence of non-linear effects
on acoustic propagation through a porous medium
saturated by a compressible isothermic fluid. It is
proved that the correction of the Darcy's acoustic law
is quadratic in terms of the pressure gradient and
originates exclusively from the convection phenomena in
the pores. This term involves a third order tensor
completely determined by the micro-structure of the
material and disappears in the case of macroscopic
isotropy.",
}
@Article{Lewinski:1985:HFE,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "On homogenization of fissured elastic plates",
journal = j-MECH-RESEARCH-COMM,
volume = "12",
pages = "271--281",
year = "1985",
CODEN = "MRCOD2",
ISSN = "0093-6413",
}
@Article{Lewinski:1986:NAS,
author = "T. Lewi{\'n}ski",
title = "A note on averaging stiffnesses of thin elastic
periodic plates",
journal = j-ENG-TRANS,
volume = "34",
pages = "337--352",
year = "1986",
CODEN = "RZINAZ",
ISSN = "0035-9408",
}
@Article{Lewinski:1988:AMHa,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Asymptotic method of homogenization of fissured
elastic plates",
journal = j-J-ELAST,
volume = "19",
pages = "37--62",
year = "1988",
CODEN = "JELSAY",
ISSN = "0374-3535",
}
@Article{Lewinski:1988:AMHb,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Asymptotic method of homogenization of two models of
elastic shells",
journal = j-ARCH-MECH,
volume = "40",
pages = "705--723",
year = "1988",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Lewinski:1988:HFRa,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Homogenization of fissured {Reissner}-like plates.
Part {I}: Method of two-scale asymptotic expansion",
journal = j-ARCH-MECH,
volume = "40",
pages = "97--117",
year = "1988",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Lewinski:1988:HFRb,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Homogenization of fissured {Reissner}-like plates.
Part {II}: Convergence",
journal = j-ARCH-MECH,
volume = "40",
pages = "119--134",
year = "1988",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Lewinski:1988:HFRc,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Homogenization of fissured {Reissner}-like plates.
Part {III}: Some particular cases and illustrative
example",
journal = j-ARCH-MECH,
volume = "40",
pages = "299--307",
year = "1988",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Lewinski:1989:OPP,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Overall properties of plates with partially
penetrating fissures",
journal = "C. R. Acad. Sci. Paris, S{\'e}rie II",
volume = "309",
pages = "951--956",
year = "1989",
}
@Article{Lewinski:1991:ACE,
author = "T. Lewi{\'n}ski",
title = "An algorithm for computing effective stiffnesses of
plates with periodic structure",
journal = j-Z-ANGE-MATH-MECH,
volume = "71",
pages = "T330--T332",
year = "1991",
CODEN = "ZAMMAX",
ISSN = "0044-2267",
}
@Article{Lewinski:1991:EMC,
author = "T. Lewi{\'n}ski",
title = "Effective models of composite periodic plates. {I} ---
Asymptotic solution. {II} --- Simplifications due to
symmetries. {III} --- Two-dimensional approaches",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "27",
pages = "1155--1172, 1173--1184, 1185--1203",
year = "1991",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Lewinski:1991:ESC,
author = "T. Lewi{\'n}ski",
title = "Effective stiffnesses of cylindrical shells of
periodic structure",
journal = j-MECH-RESEARCH-COMM,
volume = "18",
pages = "245--252",
year = "1991",
CODEN = "MRCOD2",
ISSN = "0093-6413",
}
@Article{Lewinski:1991:HEP,
author = "T. Lewi{\'n}ski and J. J. Telega",
title = "Homogenization and effective properties of plates
weakened by partially penetrating fissured: Asymptotic
analysis",
journal = j-INT-J-ENG-SCI,
volume = "29",
pages = "1129--1155",
year = "1991",
CODEN = "IJESAN",
ISSN = "0020-7225",
}
@InProceedings{Lewinski:1991:NUH,
author = "T. Lewi{\'n}ski and J. J. Telega",
editor = "W. Schneider and H. Troger and F. Ziegler",
booktitle = "Trends and Applications of Mathematics to Mechanics",
title = "Non-uniform homogenization and effective properties of
a class of nonlinear elastic shells",
publisher = "Longman",
address = "London",
pages = "248--253",
year = "1991",
}
@Article{Lewinski:1992:HSP,
author = "T. Lewi{\'n}ski",
title = "Homogenizing stiffnesses of plates with periodic
structure",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "29",
pages = "309--326",
year = "1992",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Lewinski:1992:MLS,
author = "T. Lewi{\'n}ski and St. Kucharski",
title = "A model with lenth scales for composites with periodic
structure. Steady state heat conduction problem",
journal = j-COMPUT-MECH,
volume = "9",
pages = "249--265",
year = "1992",
CODEN = "CMMEEE",
ISSN = "0178-7675",
}
@Article{Lewinski:1993:ELW,
author = "T. Lewi{\'n}ski and M. Zhou and G. I. N. Rozvany",
title = "Exact least-weight truss layouts for rectangular
domains with various support conditions",
journal = j-STRUCT-OPTIM,
volume = "6",
pages = "65--67",
year = "1993",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Lewinski:1993:RDH,
author = "T. Lewi{\'n}ski",
title = "On recent developments in the homogenization theory of
elastic plates and their application to optimal design:
Part {I}.",
journal = j-STRUCT-OPTIM,
volume = "6",
pages = "59--64",
year = "1993",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Book{Lions:1971:OCS,
author = "J. L. Lions",
title = "Optimal control systems governed by partial
differential equations",
publisher = pub-SV,
address = "Berlin",
year = "1971",
}
@Article{Lions:1997:EG,
author = "J.-L. Lions and F. Murat",
fullauthor = "Jacques-Louis Lions and F. Murat",
title = "{E. De Giorgi} (1928--1996)",
journal = j-NAMS,
volume = "44",
number = "9",
pages = "1095--1096",
year = "1997",
CODEN = "AMNOAN",
ISSN = "0002-9920",
note = "Translated from the French.",
fjournal = "Notices of the American Mathematical Society",
}
@Article{Lipton:1988:EET,
author = "R. Lipton",
title = "On the effective elasticity of a two-dimensional
homogenised incompressible elastic composite",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "110",
number = "1-2",
pages = "45--61",
year = "1988",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Lipton:1990:DLS,
author = "R. Lipton and M. Avellaneda",
title = "Darcy's law for slow viscous flow past a stationary
array of bubbles",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "114",
number = "1-2",
pages = "71--79",
year = "1990",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Lipton:1991:BEC,
author = "R. Lipton",
title = "On the behavior of elastic composites with transverse
isotropic symmetry",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "39",
number = "5",
pages = "663--681",
year = "1991",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Lipton:1992:BPS,
author = "R. Lipton",
title = "Bounds and perturbation series for incompressible
elastic composites with transverse isotropic symmetry",
journal = j-J-ELAST,
volume = "27",
number = "3",
pages = "193--225",
year = "1992",
CODEN = "JELSAY",
ISSN = "0374-3535",
fjournal = "Journal of Elasticity",
}
@TechReport{Lipton:1993:HTP,
author = "R. Lipton and B. Vernescu",
title = "Homogenization of Two Phase Emulsions with Surface
Tension Effects",
number = "1139",
institution = "Institute for Mathematics and Its Applications,
Minnesota",
year = "1993",
abstract = "We consider an emulsion of two {Stokes} fluids, one of
which is periodically distributed in the form of small
spherical bubbles. The effects of surface tension on
the bubble boundaries are modelled mathematically, as
in the work of G. I. Taylor, by a jump only in the
normal component of the traction. For a given volume
fraction of bubbles we consider the two-scale
convergence, and in the fine phase limit we find that
the bulk flow is described by an anisotropic {Stokes}
fluid. The effective viscosity tensor is consistent
with the bulk stress formula obtained by {Batchelor}.
We find a new dual variational principle describing the
effective viscosity and obtain bound on the energy
dissipation rate for periodic anisotropic emulsions.",
keywords = "homogenization, emulsions, surface tension, effective
viscosity, bounds",
}
@Article{Lipton:1993:IEE,
author = "R. Lipton",
title = "Inequalities for electric and elastic polarization
tensors with applications to random composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "41",
number = "5",
pages = "809--833",
year = "1993",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@InProceedings{Lipton:1993:IPR,
author = "R. Lipton",
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials. {Lyngby,
Denmark}",
title = "On Implementation of Partial Relaxation for Optimal
Structural Compliance Problems",
organization = "IUTAM",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "451--468",
month = "",
year = "1993",
}
@Article{Lipton:1994:HTP,
author = "R. Lipton and B. Vernescu",
title = "Homogenisation of two-phase emulsions",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "124",
number = "6",
pages = "1119--1134",
year = "1994",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Lipton:1994:OBE,
author = "R. Lipton",
title = "Optimal bounds on effective elastic tensors for
orthotropic composites",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "444",
number = "1921",
pages = "399--410",
year = "1994",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Lipton:1994:ODR,
author = "R. Lipton",
title = "Optimal Design and Relaxation for Reinforced Plates
Subject to Random Transverse Loads.",
journal = j-PROB-ENG-MECH,
volume = "9",
number = "",
pages = "167--177",
year = "1994",
CODEN = "PEMEEX",
ISSN = "0266-8920",
}
@Article{Lipton:1994:ORP,
author = "R. Lipton",
title = "On Optimal Reinforcement of Plates and Choice of
Design Parameters",
journal = j-CONTROL-CYBERN,
volume = "23",
number = "3",
pages = "481--493",
year = "1994",
CODEN = "CCYBAP",
ISSN = "0324-8569",
}
@InProceedings{Lipton:1995:MFO,
author = "R. Lipton and A. R. D{\'\i}az",
editor = "N. Olhoff and G. I. N. Rozvany",
booktitle = "Structural and Multidisciplinary Optimization,
{Goslar, Germany}",
title = "Moment Formulations for Optimum Layout in 3{D}
Elasticity.",
organization = "",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "161--168",
month = "",
year = "1995",
note = "Journal version in \cite{Diaz:1997:OML}",
}
@Article{Lipton:1995:VMS,
author = "R. Lipton and B. Vernescu",
title = "Variational methods, size effects and extremal
microgeometries for elastic composites with imperfect
interface",
journal = j-MATH-MODELS-METHODS-APPL-SCI,
volume = "5",
number = "8",
pages = "1139--1173",
year = "1995",
CODEN = "MMMSEU",
ISSN = "0218-2025",
fjournal = "Mathematical Models \& Methods in Applied Sciences",
}
@Article{Lipton:1996:CII,
author = "R. Lipton and B. Vernescu",
title = "Composites with imperfect interface",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "452",
number = "1945",
pages = "329--358",
year = "1996",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Lipton:1997:RMP,
author = "R. Lipton and A. R. D{\'\i}az",
title = "Reinforced {Mindlin} plates with extremal stiffness",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "34",
number = "28",
pages = "3691--3704",
year = "1997",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Lipton:1997:VMB,
author = "R. Lipton",
title = "Variational methods, bounds, and size effects for
composites with highly conducting interface",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "3",
pages = "361--384",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Lipton:1998:SSE,
author = "R. Lipton",
title = "The second {S}tekloff eigenvalue and energy
dissipation inequalities for functionals with surface
energy",
journal = j-SIAM-J-MATH-ANA,
volume = "29",
number = "3",
pages = "673--680 (electronic)",
year = "1998",
CODEN = "SJMAAH",
ISSN = "1095-7154",
fjournal = "SIAM Journal on Mathematical Analysis",
}
@TechReport{Lipton:19xx:BPT,
author = "R. Lipton and B. Vernescu",
title = "Bulk properties of two phase emulsions with surface
tension effects",
year = "19xx",
abstract = "We consider an emulsion of two {Stokes} fluids, one of
which is in the form of small bubbles held spherical by
surface tension. The effect of surface tension is
modeled by Taylor's conditions on the normal stress and
velocity at the two fluid interface. For a given volume
fraction of bubbles we consider the fine phase limit of
a family of periodic emulsions. We find in the
asymptotic limit that the bulk flow has a viscosity
tensor consistent with the bulk stress formula obtained
by {Batchelor} (1970). We find a new dual variational
principle describing the effective viscosity and obtain
bounds on the energy dissipation rate for periodic
anisotropic emulsions. These bounds are precisely the
arithmetic and harmonic mean of the two viscosities.",
keywords = "homogenization, emulsions, surface tension, effective
viscosity, bounds",
}
@Book{Ljusternik:1966:TCV,
author = "L. A. Ljusternik",
title = "The topology of the calculus of variations in the
large",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "vii + 96",
year = "1966",
note = "Translated from the Russian by J. Danskin.
Translations of Mathematical Monographs, Vol. 16.",
}
@PhdThesis{Lu:1993:EEM,
author = "J. Lu",
title = "Elastic energy minimization and the shape of coherent
precipitates",
school = "New York University",
address = "New York",
year = "1993",
}
@Article{Lukkassen:19xx:SSBa,
author = "D. Lukkassen and L. E. Persson and P. Wall",
fullauthor = "Dag Lukkassen and Lars Erik Persson and Peter Wall",
title = "On some sharp bounds for the homogenized p-{Poisson}
equation.",
journal = j-APPLIC-ANAL,
year = "19xx",
CODEN = "APANCC",
ISSN = "0003-6811",
note = "To appear.",
abstract = "We consider homogenization of a scale of p-{Poisson}
equations in $R^N$. Some new bounds of the effective
energy are proved and compared with the non-linear
Wiener- and Hashin-Shtrikman bounds. Moreover, we point
out concrete nontrivial examples where these bounds
even coincide. Some new examples of ``optimal''
microstructures are presented",
ams = "35B27, 35Q99, 73B27, 73K20",
keywords = "p-{Poisson} equation, homogenization, effective
energy, bounds, optimal structures, means",
}
@Article{Lukkassen:19xx:SSBb,
author = "D. Lukkassen",
fullauthor = "Dag Lukkassen",
title = "On some sharp bounds for the off-diagonal elements of
the homogenized tensor",
journal = j-APPL-MATH,
year = "19xx",
ISSN = "0862-7940",
note = "To appear.",
abstract = "In this paper we study bounds for the off-diagonal
elements of the homogenized tensor for the stationary
heat conduction problem. We also state that these
bounds are sharp by proving a formula for the
homogenized tensor in the case of laminate structures",
ams = "35B27, 35Q99, 73B27, 73K20",
keywords = "stationary heat conduction problem, $Y$-periodicity,
homogenized coefficients, bounds, laminate structures",
}
@Article{Lurie:1963:MBP,
author = "K. A. Lurie",
title = "The {Mayer-Bolza} problem for multiple integrals and
optimization of the behavior of systems with
distributed parameters",
journal = j-PRIKL-MAT-MEH,
volume = "27",
number = "2",
pages = "842--853",
year = "1963",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR88e:73020",
note = "In Russian",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@InCollection{Lurie:1967:MBP,
author = "K. A. Lurie",
editor = "G. Leitmann",
booktitle = "Topics in Optimization",
title = "The {Mayer-Bolza} problem for multiple integrals: Some
optimum problems for elliptic differential equations
arriving in magnetohydrodynamics",
publisher = pub-AP,
address = pub-AP:adr,
pages = "147--193",
year = "1967",
}
@Article{Lurie:1967:OPD,
author = "K. A. Lurie",
booktitle = "Automatic and remote control III (Proc. Third Congr.
Internat. Federation Automat. Control (IFAC), London,
1966), Vol. 1, p. 36, Paper 19A",
title = "Optimal problems for distributed systems",
publisher = "Inst. Mech. Engrs.",
address = "London",
pages = "7",
year = "1967",
}
@Article{Lurie:1970:ODR,
author = "K. A. Lurie",
title = "On the optimal distribution of the resistivity tensor
of the working medium in the channel of a {MHD}
generator",
journal = j-PRIKL-MAT-MEH,
volume = "34",
number = "2",
pages = "67--81",
year = "1970",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Book{Lurie:1970:TE,
author = "A. I. Lurie",
title = "Theory of elasticity",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
year = "1970",
note = "In {Russian}.",
}
@Article{Lurie:1971:DHO,
author = "K. A. Lurie",
title = "Discontinuities in hyperbolic optimal problems",
journal = j-J-OPT-THEORY-APPL,
volume = "7",
pages = "325--336",
year = "1971",
CODEN = "JOTABN",
ISSN = "0022-3239",
}
@Book{Lurie:1975:OCP,
author = "K. A. Lurie",
title = "Optimal control in problems of mathematical physics",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
year = "1975",
note = "In {Russian}.",
}
@Article{Lurie:1976:APT,
author = "K. A. Lurie and A. Cherkaev",
title = "On applying {Prager}'s theorem to the problems of
optimal design of thin plates",
journal = j-MECH-SOLIDS,
number = "6",
pages = "157--159",
year = "1976",
CODEN = "MESOBN",
ISSN = "0025-6544",
}
@InCollection{Lurie:1978:NBE,
author = "K. A. Lurie and A. V. Cherkaev",
booktitle = "Nonlinear problems in structural mechanics. Structural
optimization",
title = "Nonhomogeneous bar of extremal torsional rigidity",
publisher = "Naukova Dumka",
address = "Kiev, Ukraine",
pages = "64--68",
year = "1978",
}
@TechReport{Lurie:1980:CSP,
author = "K. A. Lurie and A. V. Fedorov and A. V. Cherkaev",
title = "Relaxation of optimal design problems for bars and
plates and eliminating of contradictions in the
necessary conditions of optimality",
type = "Report",
number = "667",
institution = "Ioffe Physico-technical Institute, Acad of Sc, USSR",
address = "Leningrad, USSR",
year = "1980",
note = "In Russian. English translation in
\cite{Lurie:1982:ROD}, part I.",
}
@TechReport{Lurie:1980:ESC,
author = "K. A. Lurie and A. V. Fedorov and A. V. Cherkaev",
title = "On the existence of solutions of certain optimal
design problems for bars and plates",
type = "Report",
number = "668",
institution = "Ioffe Physico-technical Institute, Acad of Sc, USSR",
address = "Leningrad, USSR",
year = "1980",
note = "In Russian. English translation in
\cite{Lurie:1982:ROD}, part II.",
}
@Article{Lurie:1981:CSA,
author = "K. A. Lurie and A. V. Cherkaev",
title = "${G}$-closure of a set of anisotropic conducting media
in the case of two dimensions",
journal = j-DOKL-AKAD-NAUK,
volume = "259",
number = "2",
pages = "328--331",
year = "1981",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRclass = "73C30 (35J15 73K20)",
MRnumber = "83b:73011",
MRreviewer = "D. Stanomir",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "In Russian",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
}
@TechReport{Lurie:1981:CSAa,
author = "K. A. Lurie and A. V. Cherkaev",
title = "${G}$-closure of a set of anisotropically conducting
media in the two-dimensional case",
type = "Report",
number = "213",
institution = "DCAMM",
address = "Technical University of Denmark",
year = "1981",
note = "Published later as \cite{Lurie:1984:CSA}",
}
@TechReport{Lurie:1981:CSP,
author = "K. A. Lurie and A. V. Cherkaev",
title = "${G}$-closure of some particular sets of admissible
material characteristics for the problem of bending of
thin elastic plates",
type = "Report",
number = "214",
institution = "DCAMM",
address = "Technical University of Denmark",
year = "1981",
note = "Published later as \cite{Lurie:1984:CSP}",
}
@TechReport{Lurie:1982:EEC,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Exact estimates of conductivity of mixtures composed
of two isotropical media taken in prescribed
proportion",
number = "Ref. 783",
institution = "Physical-Technical Institute, Acad. Sci. USSR",
year = "1982",
note = "In Russian. Published in English as
\cite{Lurie:1984:EECb}",
}
@Article{Lurie:1982:ROD,
author = "K. A. Lurie and A. V. Cherkaev and A. V. Fedorov",
title = "Regularization of optimal design problems for bars and
plates. {I}, {II}",
journal = j-J-OPT-THEORY-APPL,
volume = "37",
number = "4",
pages = "499--522, 523--543",
year = "1982",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "523--543. 73K40 (49B22)",
MRnumber = "84b:73035",
MRreviewer = "J. A. K{\"o}nig",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "The first and the second parts were separately
published as \cite{Lurie:1980:CSP} and
\cite{Lurie:1980:ESC}",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@Article{Lurie:1984:CSA,
author = "K. A. Lurie and A. V. Cherkaev",
title = "${G}$-closure of a set of anisotropically conducting
media in the two-dimensional case",
journal = j-J-OPT-THEORY-APPL,
volume = "42",
number = "2",
pages = "283--304",
year = "1984",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "73K20 (49A50 73S99)",
MRnumber = "87c:73063a",
MRreviewer = "E. S. {\c{S}}uhubi",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "First published as \cite{Lurie:1981:CSAa}. See errata
\cite{Lurie:1987:ECC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@Article{Lurie:1984:CSP,
author = "K. A. Lurie and A. V. Cherkaev",
title = "${G}$-closure of some particular sets of admissible
material characteristics for the problem of bending of
thin elastic plates",
journal = j-J-OPT-THEORY-APPL,
volume = "42",
number = "2",
pages = "305--316",
year = "1984",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "73K20 (49A50 73S99)",
MRnumber = "87c:73063b",
MRreviewer = "E. S. {\c{S}}uhubi",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "Published first as \cite{Lurie:1981:CSP}. See errata
\cite{Lurie:1987:ECC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@TechReport{Lurie:1984:EECa,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Exact estimates of conductivity of a binary mixture of
isotropic compounds",
type = "Report",
number = "894",
institution = "Ioffe Physico-technical Institute, Acad of Sc, USSR",
year = "1984",
note = "In Russian. Published in English as
\cite{Lurie:1986:EEC}",
}
@Article{Lurie:1984:EECb,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Exact estimates of conductivity of composites formed
by two isotropically conducting media taken in
prescribed proportion",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "99",
number = "1-2",
pages = "71--87",
year = "1984",
CODEN = "PEAMDU",
ISSN = "0308-2105",
MRclass = "73K20",
MRnumber = "86f:73035",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "Published earlier as \cite{Lurie:1982:EEC} (in
Russian)",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Lurie:1984:ESS,
author = "K. A. Lurie and A. V. Cherkaev and A. V. Fedorov",
title = "On the existence of solutions to some problems of
optimal design for bars and plates",
journal = j-J-OPT-THEORY-APPL,
volume = "42",
number = "2",
pages = "247--281",
year = "1984",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "73K40 (49A50 73K20)",
MRnumber = "85f:73079",
MRreviewer = "Vadim Komkov",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@Article{Lurie:1984:GCS,
author = "K. A. Lurie and A. V. Cherkaev",
title = "{G-closure} of some particular sets of admissible
material characteristics for the problem of bending of
thin plates",
journal = j-J-OPT-THEORY-APPL,
volume = "42",
pages = "305--316",
year = "1984",
CODEN = "JOTABN",
ISSN = "0022-3239",
}
@Article{Lurie:1985:OPM,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Optimization of properties of multicomponent isotropic
composites",
journal = j-J-OPT-THEORY-APPL,
volume = "46",
number = "4",
pages = "571--580",
year = "1985",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "73K20 (49A34 73U05)",
MRnumber = "86j:73066",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@Article{Lurie:1986:ECC,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Effective characteristics of composite materials and
the optimal design of structural elements. (Russian)",
journal = j-USP-MEH,
volume = "9",
pages = "3--81",
year = "1986",
CODEN = "USMEEG",
ISSN = "0137-3722",
note = "English translation in \cite{Lurie:1997:ECC}",
}
@Article{Lurie:1986:EEC,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Exact estimates of the conductivity of a binary
mixture of isotropic materials",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "104",
number = "1-2",
pages = "21--38",
year = "1986",
CODEN = "PEAMDU",
ISSN = "0308-2105",
MRclass = "73B99 (35Q20)",
MRnumber = "88e:73004",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "Published earlier as \cite{Lurie:1984:EECa}",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Article{Lurie:1987:ECC,
author = "K. A. Lurie and A. V. Cherkaev",
title = "Errata corrig{\'e}. {On} ${G}$-closure:
``${G}$-closure of a set of anisotropically conducting
media in the two-dimensional case'' [{J}. {Optim}.\
{Theory} {Appl}.\ {\bf 42} (1984), no.\ 2, 283--304;
{MR} 87c:73063a] and ``${G}$-closure of some particular
sets of admissible material characteristics for the
problem of bending of thin elastic plates'' [ibid.\
{\bf 42} (1984), no.\ 2, 305--316; {MR} 87c:73063b]",
journal = j-J-OPT-THEORY-APPL,
volume = "53",
number = "2",
pages = "319--327",
year = "1987",
CODEN = "JOTABN",
ISSN = "0022-3239",
MRclass = "73K20 (49A22 73S99)",
MRnumber = "88j:73044",
MRreviewer = "E. S. {\c{S}}uhubi",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
note = "See \cite{Lurie:1984:CSA,Lurie:1984:CSP}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
}
@InProceedings{Lurie:1988:CVP,
author = "K. A. Lurie and A. V. Cherkaev",
editor = "J. M. Ball",
booktitle = "Material instabilities in continuum mechanics
(Edinburgh, 1985--1986)",
title = "On a certain variational problem of phase
equilibrium",
publisher = "Oxford Sci. Publ., Oxford Univ. Press",
address = "New York",
pages = "257--268",
year = "1988",
MRclass = "73C60 (49A50 80A20 82A25)",
MRnumber = "90a:73044",
MRreviewer = "Luciano Modica",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
}
@Article{Lurie:1988:OFH,
author = "L. V. Gibiansky K. A. Lurie and A. V. Cherkaev",
title = "Optimal focusing of heat flow by heterogeneous
heat-conducting media (thermo-lens problem)",
journal = j-Z-TEH-FIZ,
volume = "58",
number = "1",
pages = "67--74",
year = "1988",
CODEN = "ZTEFA3",
ISSN = "0044-4642",
}
@Article{Lurie:1990:EOP,
author = "K. A. Lurie",
title = "The extension of optimisation problems containing
controls in the coefficients",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "114",
number = "1-2",
pages = "81--97",
year = "1990",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Book{Lurie:1990:NTE,
author = "A. I. Lurie",
title = "Nonlinear theory of elasticity",
publisher = pub-NH,
address = pub-NH:adr,
pages = "xiv + 617",
year = "1990",
ISBN = "0-444-87439-9",
note = "Translated from the Russian by K. A. Lurie.",
}
@InCollection{Lurie:1991:GCO,
author = "K. A. Lurie",
booktitle = "Mathematics of random media (Blacksburg, VA, 1989)",
title = "On a general concept in optimal material layout",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "301--321",
year = "1991",
}
@Article{Lurie:1992:DSOa,
author = "K. A. Lurie",
title = "Direct solution of an optimal layout problem for
isotropic and anisotropic heat conductors on a plane",
journal = j-J-OPT-THEORY-APPL,
volume = "72",
number = "3",
pages = "553--575",
year = "1992",
CODEN = "JOTABN",
ISSN = "0022-3239",
fjournal = "Journal of Optimization Theory and Applications",
}
@InProceedings{Lurie:1992:DSOb,
author = "K. A. Lurie and R. Lipton",
booktitle = "Theoretical aspects of industrial design
(Wright-Patterson Air Force Base, OH, 1990)",
title = "Direct solution of an optimal layout problem for
isotropic heat conductors in three dimensions",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "1--11",
year = "1992",
}
@Book{Lurie:1993:AOC,
author = "K. A. Lurie",
title = "Applied Optimal Control Theory of Distributed
Systems",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "xii + 499",
year = "1993",
ISBN = "0-306-43993-X",
series = "",
}
@Article{Lurie:1994:DRO,
author = "K. A. Lurie",
title = "Direct relaxation of optimal layout problems for
plates",
journal = j-J-OPT-THEORY-APPL,
volume = "80",
number = "1",
pages = "93--116",
year = "1994",
CODEN = "JOTABN",
ISSN = "0022-3239",
fjournal = "Journal of Optimization Theory and Applications",
}
@InCollection{Lurie:1995:DRO,
author = "K. A. Lurie",
booktitle = "Recent trends in optimization theory and
applications",
title = "On direct relaxation of optimal material design
problems for plates",
publisher = "World Sci. Publishing",
address = "River Edge, NJ",
pages = "271--296",
year = "1995",
}
@InCollection{Lurie:1997:ECC,
author = "K. A. Lurie and A. V. Cherkaev",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "Effective characteristics of composite materials and
the optimal design of structural elements [partial
translation of {MR} 88e:73019]",
volume = "31",
publisher = "Birkh{\"{a}}user",
address = "Boston, MA",
pages = "175--258",
year = "1997",
note = "Translation. Originally published as
\cite{Lurie:1986:ECC}",
series = "Progress in nonlinear differential equations and their
applications",
xxbooktitle = "Topics in the mathematical modeling of composite
materials",
}
@Article{Lurie:1997:EPS,
author = "K. A. Lurie",
title = "Effective properties of smart elastic laminates and
the screening phenomenon",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "34",
number = "13",
pages = "1633--1643",
year = "1997",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@InCollection{Lurie:1997:LCM,
author = "K. A. Lurie and T. Y. Simkina",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "Load characteristics of a {MHD} channel in the case of
optimal distribution of the resistivity of the working
medium",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "259--271",
year = "1997",
}
@InCollection{Lurie:1997:STC,
author = "K. A. Lurie",
booktitle = "Optimization methods in partial differential equations
(South Hadley, MA, 1996)",
title = "Spatio-temporal control in the coefficients of linear
hyperbolic equations",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "177--182",
year = "1997",
}
@Article{Luskin:1992:AFE,
author = "M. Luskin and Ling Ma",
title = "Analysis of the finite element approximation of
microstructure in micromagnetics",
journal = j-SIAM-J-NUMER-ANAL,
volume = "29",
number = "2",
pages = "320--331",
year = "1992",
CODEN = "SJNAAM",
ISSN = "0036-1429",
MRnumber = "MR92m:65147",
fjournal = "SIAM Journal on Numerical Analysis",
}
@Article{Luskin:1996:ALM,
author = "M. Luskin",
title = "Approximation of a laminated microstructure for a
rotationally invariant, double well energy density",
journal = j-NUM-MATH,
volume = "75",
number = "2",
pages = "205--221",
year = "1996",
CODEN = "NUMMA7",
ISSN = "0029-599X",
MRnumber = "MR97k:73026",
fjournal = "Numerische Mathematik",
}
@InCollection{Luskin:1996:CCM,
author = "M. Luskin",
booktitle = "Acta numerica, 1996",
title = "On the computation of crystalline microstructure",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "191--257",
year = "1996",
MRnumber = "MR1624603",
}
@Article{Lutoborski:1982:EME,
author = "A. Lutoborski and J. J. Telega",
title = "Effective moduli for an elastic arch",
journal = "Bull. Acad. Pol. Sci., Serie Sci. Tech.",
volume = "30",
pages = "165--170",
year = "1982",
}
@Article{Lutoborski:1984:HPE,
author = "A. Lutoborski and J. J. Telega",
title = "Homogenization of a plane elastic arch",
journal = j-J-ELAST,
volume = "14",
pages = "65--77",
year = "1984",
CODEN = "JELSAY",
ISSN = "0374-3535",
}
@InProceedings{Ma:1992:TSO,
author = "Z. D. Ma and N. Kikuchi and H. C. Cheng and I
Hagiwara",
editor = "",
booktitle = "ASME Winter Annular Meeting",
title = "Topology and Shape Optimization Technique for Free
Vibration Problems",
organization = "{ASME, 1992}",
publisher = "",
address = "{Anaheim}, {California}",
pages = "127--138",
month = "",
year = "1992",
}
@InProceedings{Ma:1993:TSO,
author = "Z. D. Ma and N. Kikuchi and H. C. Cheng and I
Hagiwara",
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials, Lyngby,
Denmark",
title = "Topology and Shape Optimization Technique for
Structural Dynamic Problems",
organization = "{IUTAM}",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "247--261",
month = "",
year = "1993",
}
@Book{Makarets:1995:ODE,
author = "M. V. Makarets and V. Yu. Reshetnyak",
title = "Ordinary differential equations and calculus of
variations",
publisher = "World Scientific Publishing Co. Inc.",
address = "River Edge, NJ",
pages = "x + 372",
year = "1995",
ISBN = "981-02-2191-6",
note = "Book of problems.",
}
@Article{Marcellini:1985:AQF,
author = "P. Marcellini",
title = "Approximation of quasiconvex functions, and lower
semicontinuity of multiple integrals",
journal = j-MANUSCR-MATH,
volume = "51",
number = "1-3",
pages = "1--28",
year = "1985",
CODEN = "MSMHB2",
ISSN = "0025-2611",
fjournal = "Manuscripta Mathematica",
}
@Article{Marino:1969:TAD,
author = "A. Marino and S. Spagnolo",
title = "Un tipo di approssimazione dell'operatore $\sum\sb
1\sp nij {D}\sb i(a\sb {ij}(x){D}\sb j)$ con operatori
$\sum\sb 1\sp nj{D}\sb j(\beta (x){D}\sb j)$",
journal = "Ann. Scuola Norm. Sup. Pisa (3)",
volume = "23",
pages = "657--673",
year = "1969",
MRnumber = "43:3859",
}
@Article{Markenscoff:1997:SEI,
author = "X. Markenscoff",
title = "On the shape of the {Eshelby} inclusions",
journal = j-J-ELAST,
volume = "49",
number = "2",
pages = "163--166",
year = "1997/98",
CODEN = "JELSAY",
ISSN = "0374-3535",
fjournal = "Journal of Elasticity",
}
@Article{Markenscoff:1998:WPC,
author = "X. Markenscoff and M. Paukshto",
title = "The wedge paradox and a correspondence principle",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "454",
number = "1968",
pages = "147--154",
year = "1998",
CODEN = "PRLAAZ",
ISSN = "1364-5021",
fjournal = "The Royal Society of London. Proceedings. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Markov:1996:SDH,
author = "K. Z. Markov and D. R. S. Talbot and J. R. Willis",
title = "On stationary diffusion in heterogeneous media",
journal = j-IMA-J-APPL-MATH,
volume = "56",
number = "2",
pages = "133--144",
year = "1996",
CODEN = "IJAMDM",
ISSN = "0272-4960",
fjournal = "IMA Journal of Applied Mathematics",
}
@Book{Markov:1999:HMM,
editor = "K. Markov and L. Preziosi",
title = "Heterogeneous Media: Micromechanics Modelling Methods
and Simulation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
year = "1999",
ISBN = "",
LCCN = "",
}
@Book{Markushevich:1985:TFC,
author = "A. I. Markushevich",
title = "Theory of functions of a complex variable",
publisher = "Chelsea Publishing Company",
address = "New York",
edition = "Second",
year = "1985",
}
@Book{Marsden:1994:MFE,
author = "Jerrold E. Marsden and Thomas J. R. Hughes",
title = "Mathematical foundations of elasticity",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 556",
year = "1994",
ISBN = "0-486-67865-2",
note = "Corrected reprint of the 1983 original.",
}
@TechReport{Maso:1993:CTN,
author = "G. {Dal Maso} and A. Garroni",
title = "Capacity Theory for Non-Symmetric Elliptic Operators",
number = "179/M",
institution = "SISSA ISAS",
year = "1993",
abstract = "We study the properties of the capacity $ \mbox{cap}^L
(A, \Omega)$ with respect to an arbitrary, possibly
non-symmetric, elliptic operator $L$.",
}
@Book{Maso:1993:IC,
author = "G. {Dal Maso}",
title = "An introduction to ${\Gamma}$-convergence",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xiv + 340",
year = "1993",
ISBN = "0-8176-3679-X",
}
@TechReport{Maso:1993:NAS,
author = "G. {Dal Maso} and A. Garroni",
fullauthor = "G. {Dal Maso} and Adriana Garroni",
title = "A new approach to the study of limits of {Dirichlet}
problems in perforated domains",
number = "67/M",
institution = "SISSA ISAS",
year = "1993",
abstract = "Let $A$ be a linear elliptic operator of the second
order with bounded measurable coefficients on a bounded
open set $ \Omega$ of $R^n$, and let $(\Omega_h)$ be an
arbitrary sequence of open subsets of $\Omega$. We
prove the following compactness result: there exist a
subsequence, still denoted by $(\Omega_h)$, and a
positive Borel measure $\mu$ on $\Omega$, not charging
polar sets, such that, for every $f \in H^{-1}
(\Omega)$, the solutions $u_h \in H{^{1}_{0}}
(\Omega_h)$ of the equations $Au_h = f$ in $\Omega_h$,
extended to $0$ on $\Omega \setminus \Omega_h$,
converge weakly in $H{^{1}_{0}} (\Omega)$ to the unique
solution $u \in H{^{1}_{0}} (\Omega) \cap L{^{2}_{\mu}
(\Omega)}$ of the problem $$ \langle Au, v \rangle +
\int_\Omega uvd \mu = \langle f, v \rangle \ \ \
\forall v \in H{^{1}_{0}} (\Omega) \cap L{^{2}_{\mu}}
(\Omega).$$ When $A$ is symmetric, this compactness
result is already known and was obtained by
$\Gamma$-convergence techniques. Our new proof, based
on the method of oscillating test functions, extends
the result to the non-symmetric case. The new
technique, which is completely independent of
$\Gamma$-convergence, relies on the study of the
behaviour $w{^{*}_{h}} \in H{^{1}_{0}} (\Omega_h)$ of
the equations $A^* w{^{*}_{h}} = 1$ in $\Omega_h$,
where $A^*$ is the adjoint operator. We prove also that
the limit measure $\mu$ does not change if $A$ is
replaced by $A^*$. Moreover, we prove that $\mu$
depends only on the symmetric part of the operator $A$,
if the coefficients of the skew-symmetric part are
continuous, while an explicit example shows that $\mu$
may depend also on the skew-symmetric part of $A$, when
the coefficients are discontinuous.",
}
@TechReport{Maso:1994:CMA,
author = "G. {Dal Maso} and A. Garroni",
fullauthor = "G. {Dal Maso} and Adriana Garroni",
title = "The Capacity Method for Asymptotic {Dirichlet}
Problems",
number = "101/94/M",
institution = "SISSA ISAS",
year = "1994",
abstract = "We prove that the asymptotic behaviour of the
solutions of {Dirichlet} problems for linear elliptic
equations in perforated domains of the form $\Omega_h =
\Omega \setminus E_h$ is uniquely determined by the
asymptotic behaviour, as $h \longrightarrow \infty$, of
suitable capacities of the sets $B \cap E_h$, where $B$
runs in a conveniently large class of subsets of
$\Omega$.",
}
@TechReport{Maso:1994:DPP,
author = "G. {Dal Maso} and F. Murat",
title = "{Dirichlet} Problems in Perforated Domains for
Homogeneous Monotone Operators on ${H_0^1}$",
number = "3/94/M",
institution = "SISSA ISAS",
year = "1994",
abstract = "Let $Au = -div (a(x, Du))$ be monotone operator acting
on $H{_{0}^{1}}(\Omega), \Omega \subseteq R^N$, where
$a(x, \xi)$ satisfies the usual hypotheses and is
homogeneous of degree one in $\xi$. Given a sequence
$(\Omega_n)$ of open subsets of $\Omega$, for every $f
\in H^{-1}(\Omega)$ we study the asymptotic behaviour,
as $n \longrightarrow \infty$, of the solutions $u_n$
of the {Dirichlet} problems: $u_n \in
H{_{0}^{1}}(\Omega_n), \ Au_n = f \ \mbox{in} \
D'(\Omega_n)$. We determine the general form of the
limit problem without any hypothesis on the sequence
$(\Omega_n)$ and we prove a corrector result.",
}
@TechReport{Maso:1994:LDP,
author = "G. {Dal Maso} and R. Toader",
fullauthor = "G. {Dal Maso} and Rodica Toader",
title = "Limits of {Dirichlet} problems in perforated domains:
a new formulation",
number = "167/94/M",
institution = "S.I.S.S.A.",
year = "1994",
abstract = "Let $A$ be a linear elliptic operator of the second
order with bounded measurable coefficients on a bounded
open set $\Omega$ of $R^n$, and let $\Omega_h$ be an
arbitrary sequence of open subsets of $\Omega$. We
prove the following compactness result: there exist a
subsequence, still denoted by $\Omega_h$, and a
function $$ w^* \in \ K^* = \{ w^* \in \
H{_{0}^{1}}(\Omega): A^* w^* \le 1 \ \mbox{in} \
{\cal{D'}} (\Omega), \ {\mbox{and}} \ w^* \ge 0 \
\mbox{a.e.} \ {\mbox{in}} \ \Omega \}$$ such that, for
every $f \in L^\infty (\Omega)$, the solutions $u_h \in
H{_{0}^{1}} (\Omega_h)$ of the equation $Au_h = f$ in
$\Omega_h$, extended by zero on $\Omega \setminus
\Omega_h$, converge weakly in $H{_{0}^{1}}(\Omega)$ to
the unique solution $u$ of the problem ?? hier fehlt
array We provide a self-contained study of the
properties of the solutions of $(*)$. We prove also the
following density result: for any $w^* \in K^*$ there
exists a sequence $\Omega_h$ of open subsets of
$\Omega$ such that for every $f \in L^\infty (\Omega)$
the solutions $u_h \in H{_{0}^{1}} (\Omega_h)$ of the
equation $Au_h = f$ in $\Omega_h$, extended by zero on
$\Omega \setminus \Omega_h$, converge weakly in
$H_0^1(\Omega)$ to the solution of $(*)$.",
}
@TechReport{Maso:1995:CTM,
author = "G. {Dal Maso} and I. V. Skrypnik",
fullauthor = "G. {Dal Maso} and Igor V. Skrypnik",
title = "Capacity Theory for Monotone Operators",
number = "6/95/M",
institution = "S.I.S.S.A. ISAS",
address = "Trieste, Italy",
month = jan,
year = "1995",
note = "$F$.",
abstract = "If $Au = - div(a(x, Du))$ is a monotone operator
defined on the Sobolev space $W^{1,p} ({\bf R^n}), 1 <
p < + \infty$, with $a(x,0) = 0 $ for a.e. $x \in {\bf
R^n}$, the capacity $C_{A}(E, F)$ relative to $A$ can
be defined for every pair $(E, F)$ of bounded sets in
${\bf R^n}$ with $E \subset F. $ We prove that $C_A
(E,F)$ is increasing and countably subadditive with
respect to $E$ and decreasing with respect to $F$.
Moreover we investigate the continuity properties of
$C_A (E,F)$ with respect to $E$ and $F$.",
}
@Article{Maso:1995:DWS,
author = "G. {Dal Maso} and P. G. Lefloch and F. Murat",
fullauthor = "G. {Dal Maso} and Philippe G. Lefloch and F. Murat",
title = "Definition and weak stability of nonconservative
products",
journal = j-J-MATH-PURES-APPL,
volume = "74",
number = "6",
pages = "483--548",
year = "1995",
CODEN = "JMPAAM",
ISSN = "0021-7824",
fjournal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es.
Neuvi{\'e}me S{\'e}rie",
}
@Article{Maso:1997:ABC,
author = "G. {Dal Maso} and F. Murat",
title = "Asymptotic behaviour and correctors for {Dirichlet}
problems in perforated domains with homogeneous
monotone operators",
journal = j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
volume = "24",
number = "2",
pages = "239--290",
year = "1997",
CODEN = "PSNAAI",
ISSN = "0391-173X",
fjournal = "Annali della Scuola Normale Superiore di Pisa. Classe
di Scienze. Serie IV",
}
@Article{Maso:1998:AEC,
author = "G. {Dal Maso} and F. Murat",
title = "Almost everywhere convergence of gradients of
solutions to nonlinear elliptic systems",
journal = j-NONLINEAR-ANAL,
volume = "31",
number = "3-4",
pages = "405--412",
year = "1998",
CODEN = "NOANDD",
ISSN = "0362-546X",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal",
}
@Article{Masur:1970:OSS,
author = "E. F. Masur",
title = "Optimum Stiffness and Strength of Elastic Structures",
journal = j-J-ENG-MECH,
volume = "96",
number = "",
pages = "621--640",
year = "1970",
CODEN = "JENMDT",
ISSN = "0733-9399",
}
@Article{Masur:1979:NSO,
author = "E. F. Masur and Z. Mroz",
title = "Non-Stationarity Optimality Conditions in Structural
Design",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "15",
number = "",
pages = "503--512",
year = "1979",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@InProceedings{Masur:1980:SSS,
author = "E. F. Masur and Z. Mroz",
editor = "S. {Nemat-Nasser}",
booktitle = "Variational Methods in the Mechanics of Solids",
title = "Singular Solutions in Structural Optimization
Problems",
publisher = "Pergamon Press",
address = "New York",
pages = "337--343",
month = "",
year = "1980",
confaddress = "Evanston, Illinois",
}
@Article{Masur:1984:SDU,
author = "E. F. Masur",
title = "On Structural Design Under Multiple Eigenvalue
Constraints",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "20",
number = "",
pages = "211--231",
year = "1984",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Masur:1985:SAC,
author = "E. F. Masur",
title = "Some Additional Comments On Structural Design Under
Multiple Eigenvalue Constraints",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "21",
number = "",
pages = "117--120",
year = "1985",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Matos:1992:YMA,
author = "J. P. Matos",
fullauthor = "Jo{\~a}o Palhoto Matos",
title = "Young measures and the absence of fine microstructures
in a class of phase transitions",
journal = j-EUR-J-APPL-MATH,
volume = "3",
number = "1",
pages = "31--54",
year = "1992",
ISSN = "0956-7925",
fjournal = "European Journal of Applied Mathematics",
}
@Book{Maugin:1993:MIE,
author = "G{\'e}rard A. Maugin",
title = "Material inhomogeneities in elasticity",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "xii + 276",
year = "1993",
ISBN = "0-412-49520-1",
}
@Article{McPhedran:1987:TPT,
author = "R. C. Mc{Phedran} and G. W. Milton",
title = "Transport properties of touching cylinder pairs and of
the square array of touching cylinders",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "411",
pages = "313--326",
year = "1987",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
}
@TechReport{Mekkaoui:19xx:EEH,
author = "T. Mekkaoui and C. Picard",
title = "Error estimates for the homogenization of a
quasilinear {Dirichlet} problem in a periodically
perfored domain",
year = "19xx",
xxnote = "Check: perfored??",
}
@Article{Mendelson:1975:ECT,
author = "K. S. Mendelson",
title = "Effective conductivities of two-phase material with
cylindrical phase boundaries",
journal = j-J-APPL-PHYS,
volume = "46",
pages = "917--918",
year = "1975",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Mendelson:1975:TCT,
author = "K. S. Mendelson",
title = "A theorem on the conductivity of two-dimensional
heterogeneous medium",
journal = j-J-APPL-PHYS,
volume = "46",
pages = "4740--4741",
year = "1975",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Michell:1899:DDS,
author = "J. H. Michell",
title = "On the direct determination of stress in an elastic
Solid, with application to the theory of Plates",
journal = j-PROC-LONDON-MATH-SOC,
volume = "31",
pages = "100--125",
year = "1899",
CODEN = "PLMTAL",
ISSN = "0024-6115",
}
@Article{Miettinen:1997:FEA,
author = "M. Miettinen and J. Haslinger",
title = "Finite element approximation of vector-valued
hemivariational problems",
journal = j-J-GLOBAL-OPT,
volume = "10",
number = "1",
pages = "17--35",
year = "1997",
CODEN = "JGOPEO",
ISSN = "0925-5001",
MRnumber = "MR98a:49018",
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
}
@Article{Miettinen:1998:FEA,
author = "M. Miettinen and J. Haslinger",
title = "Finite element approximation of parabolic
hemivariational inequalities",
journal = j-NUMER-FUNCT-ANAL-OPTIM,
volume = "19",
number = "5-6",
pages = "565--585",
year = "1998",
CODEN = "NFAODL",
ISSN = "0163-0563",
MRnumber = "MR1636470",
fjournal = "Numerical Functional Analysis and Optimization. An
International Journal",
}
@Article{Mikelic:1994:HHE,
author = "A. Mikeli{\'c} and M. Primicerio",
fullauthor = "Andro Mikeli{\'c} and Mario Primicerio",
title = "Homogenization of the Heat Equation for a Domain with
a Network of Pipes with a Well-Mixed Fluid",
journal = j-ANN-MAT-PURA-APPL-4,
volume = "CLXVI",
pages = "227--251",
year = "1994",
CODEN = "ANLMAE",
ISSN = "0373-3114",
abstract = "We consider the linear heat equation in a domain
occupied by a solid material with a network of pipes in
which a well-mixed fluid is circulating. The
temperature of the fluid in the pipe is uniform and its
time variation is determined by the thermal flux on the
wall of the pipe, plus a given internal source;
continuity of the temperature across the pipe is also
assumed. We suppose that we deal with a periodic
geometry, with cells of size $\epsilon$ with inclusions
of size $r_\epsilon$; we study in detail in the case
$r_\epsilon \sim \epsilon$, referring to a previous
paper for the case $r_\epsilon << \epsilon$. In the
limit $\epsilon \longrightarrow 0$ we get a homogenized
equation. The limit depends strongly on the ratio
between the time variation of the temperature in the
inclusions and the thermal flux through the interface.
The homogenized equation has a new specific heat, which
depends on the porosity and the constant of
proportionality between the time variation of
temperature and the flux on the boundary of the pipe.
We also have a new thermal conductivity depending on
the microstructure, and volume sources appear. The main
tool is the energy method and we generalize the
classical results for the more standard boundary
conditions for parabolic equations. Finally, we
consider the network of pipes forming a random ball
structure. We prove convergence for this case. The
homogenized equation is of the same form as in the
periodic case but auxiliary problems are stochastic.",
}
@Article{Mikelic:19xx:MDP,
author = "A. Mikeli{\'c} and R. Tapiero",
title = "Mathematical derivation of the power law describing
polymer flow through a thin slab",
volume = "??",
number = "??",
pages = "??--??",
month = "??",
year = "19xx",
}
@Book{Mikhlin:1964:IET,
author = "S. G. Mikhlin",
title = "Integral equations and their applications to certain
problems in mechanics, mathematics and technology",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
edition = "Second",
year = "1964",
}
@Book{Mikhlin:1964:VMM,
author = "S. G. Mikhlin",
title = "Variational methods in mathematical physics",
publisher = "The Macmillan Co.",
address = "New York",
pages = "xxxii + 582",
year = "1964",
note = "Translated by T. Boddington; editorial introduction by
L. I. G. Chambers. A Pergamon Press Book",
}
@Article{Milgrom:1989:LRP,
author = "M. Milgrom and S. Shtrikman",
title = "Linear response of polycrystals to coupled fields:
{Exact} relations among the coefficients",
journal = j-PHYS-REV-B,
volume = "40",
number = "9",
pages = "5991--5994",
year = "1989",
CODEN = "PLRBAQ",
ISSN = "0556-2805",
}
@Article{Milgrom:1989:LRT,
author = "M. Milgrom and S. Shtrikman",
title = "Linear response of two-phase composites with cross
moduli: {Exact} universal relations",
journal = j-PHYS-REV-A,
volume = "40",
number = "3",
pages = "1568--1575",
year = "1989",
CODEN = "PLRAAN",
ISSN = "1050-2947",
}
@Article{Milgrom:1997:SME,
author = "M. Milgrom",
title = "Some more exact results concerning multifield moduli
of two-phase composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "3",
pages = "399--404",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Milton:1980:BCD,
author = "G. W. Milton",
title = "Bounds on complex dielectric constant of a composite
material",
journal = j-APPL-PHYS-LET,
volume = "37",
number = "3",
pages = "300--302",
year = "1980",
CODEN = "APPLAB",
ISSN = "0003-6951",
}
@Article{Milton:1981:BCP,
author = "G. W. Milton",
title = "Bounds on the complex permittivity of a two-component
composite material",
journal = j-J-APPL-PHYS,
volume = "52",
pages = "5286--5293",
year = "1981",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Milton:1981:BEE,
author = "G. W. Milton",
title = "Bounds on the electromagnetic, elastic and other
properties of two-component composites",
journal = j-PHYS-REV-LET,
volume = "46",
number = "8",
pages = "542--545",
year = "1981",
CODEN = "PRLTAO",
ISSN = "0031-9007",
}
@Article{Milton:1981:BTP,
author = "G. W. Milton",
title = "Bounds on the transport and optical properties of a
two-component composite material",
journal = j-J-APPL-PHYS,
volume = "52",
pages = "5294--5304",
year = "1981",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Milton:1981:CBT,
author = "G. W. Milton",
title = "Concerning bounds on transport and mechanical
properties of multicomponent composite materials",
journal = j-APPL-PHYS,
volume = "A26",
pages = "125--130",
year = "1981",
}
@Article{Milton:1981:CTM,
author = "G. W. Milton and R. C. Mc{Phedran}",
title = "A comparison of two methods for deriving bounds on the
effective conductivity of composites",
journal = j-LECT-NOTES-PHYSICS,
volume = "154",
pages = "183--193",
year = "1981",
CODEN = "LNPHA4",
ISSN = "0075-8450",
}
@Article{Milton:1982:BET,
author = "G. W. Milton",
title = "Bounds on the elastic and transport properties of
two-component composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "30",
number = "3",
pages = "177--191",
year = "1982",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Milton:1983:CFD,
author = "G. W. Milton and M. E. Fisher",
title = "Continuum fluids with a discontinuity in the
pressure",
journal = j-J-STAT-PHYS,
volume = "32",
number = "2",
pages = "413--438",
year = "1983",
CODEN = "JSTPSB",
ISSN = "0022-4715",
fjournal = "Journal of Statistical Physics",
}
@Article{Milton:1985:CPA,
author = "G. W. Milton",
title = "The coherent potential approximation is a realizable
effective medium scheme",
journal = j-COMMUN-MATH-PHYS,
volume = "99",
number = "4",
pages = "463--500",
year = "1985",
CODEN = "CMPHAY",
ISSN = "0010-3616",
fjournal = "Communications in Mathematical Physics",
}
@InProceedings{Milton:1985:TCC,
author = "G. W. Milton and K. Golden",
booktitle = "Thermal Conductivity",
title = "Thermal conduction in composites",
volume = "18",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "571--582",
year = "1985",
}
@InProceedings{Milton:1986:MPC,
author = "G. W. Milton",
editor = "J. Ericksen and others",
booktitle = "Homogenization and Effective Moduli of Materials and
Media (Minneapolis, Minn., 1984/1985)",
title = "Modelling the properties of composites by laminates",
publisher = pub-SV,
address = pub-SV:adr,
pages = "150--175",
year = "1986",
xxpages = "150--174",
xxtitle = "Modeling the properties of composites by laminates",
}
@Article{Milton:1987:MCEa,
author = "G. W. Milton",
title = "Multicomponent composites, electrical networks and new
types of continued fraction. {I}",
journal = j-COMMUN-MATH-PHYS,
volume = "111",
number = "2",
pages = "281--327",
year = "1987",
CODEN = "CMPHAY",
ISSN = "0010-3616",
fjournal = "Communications in Mathematical Physics",
}
@Article{Milton:1987:MCEb,
author = "G. W. Milton",
title = "Multicomponent composites, electrical networks and new
types of continued fraction. {II}",
journal = j-COMMUN-MATH-PHYS,
volume = "111",
number = "3",
pages = "329--372",
year = "1987",
CODEN = "CMPHAY",
ISSN = "0010-3616",
fjournal = "Communications in Mathematical Physics",
}
@Unpublished{Milton:1988:PC,
author = "G. W. Milton",
title = "Private communication",
year = "1988",
}
@Article{Milton:1988:VBE,
author = "G. W. Milton and R. V. Kohn",
title = "Variational bounds on the effective moduli of
anisotropic composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "36",
number = "6",
pages = "597--629",
year = "1988",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@InCollection{Milton:1990:BRT,
author = "G. W. Milton",
booktitle = "Continuum models and discrete systems, Vol.\ 1 (Dijon,
1989)",
title = "A brief review of the translation method for bounding
effective elastic tensors of composites",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "60--74",
year = "1990",
}
@Article{Milton:1990:CSP,
author = "G. W. Milton",
title = "On characterizing the set of possible effective
tensors of composites: the variational method and the
translation method",
journal = j-COMM-PURE-APPL-MATH,
volume = "43",
number = "1",
pages = "63--125",
year = "1990",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Milton:1990:RCF,
author = "G. W. Milton and K. Golden",
title = "Representations for the conductivity functions of
multicomponent composites",
journal = j-COMM-PURE-APPL-MATH,
volume = "43",
number = "5",
pages = "647--671",
year = "1990",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@InProceedings{Milton:1991:FER,
author = "G. W. Milton",
booktitle = "Composite Media and Homogenization Theory",
title = "Thermal conduction in composites",
volume = "5",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "223--245",
year = "1991",
series = "Progress in Non-linear Differential Equations and
Their Applications",
}
@InCollection{Milton:1991:FERa,
author = "G. W. Milton",
booktitle = "Composite media and homogenization theory (Trieste,
1990)",
title = "The field equation recursion method",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "223--245",
year = "1991",
}
@InProceedings{Milton:1991:PLG,
author = "G. W. Milton",
booktitle = "Advances in Multiphase Flow and Related Problems",
title = "A proof that laminates generates all possible
effective conductivity functions of two dimensional
two-phase materials",
volume = "5",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "136--146",
year = "1991",
series = "Progress in Non-linear Differential Equations and
Their Applications",
}
@Article{Milton:1992:CMP,
author = "G. W. Milton",
title = "Composite materials with {Poisson}'s ratios close to
$-1$",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "40",
number = "5",
pages = "1105--1137",
year = "1992",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Milton:1994:LBS,
author = "G. W. Milton",
title = "A link between sets of tensors stable under lamination
and quasiconvexity",
journal = j-COMM-PURE-APPL-MATH,
volume = "47",
number = "7",
pages = "959--1003",
year = "1994",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
fjournal = "Communications on Pure and Applied Mathematics",
}
@Article{Milton:1995:CBP,
author = "G. W. Milton and A. B. Movchan",
title = "A correspondence between plane elasticity and the
two-dimensional real and complex dielectric equations
in anisotropic media",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "450",
number = "1939",
pages = "293--317",
year = "1995",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Milton:1995:WET,
author = "G. W. Milton and A. V. Cherkaev",
title = "What elasticity tensors are realizable?",
journal = j-J-ENG-MATER-TECHNOL,
volume = "117",
number = "4",
pages = "483--493",
year = "1995",
CODEN = "JEMTA8",
ISSN = "0094-4289",
xxtitle = "Which elasticity tensors are realizable?",
}
@InCollection{Milton:1997:CMM,
author = "G. W. Milton",
editor = "T. Tatsumi and E. Watanabe and T. Kambe",
booktitle = "Theoretical and applied mechanics (Proc. of the XIX
International Congress of Theoretical and Applied
mechanics, Kyoto, 1996)",
title = "Composites: {A} myriad of microstructure independent
relations",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "443--459",
year = "1997",
}
@Article{Milton:1997:EVM,
author = "G. W. Milton and J. G. Berryman",
title = "On the effective viscoelastic moduli of two-phase
media. {II}. {Rigorous} bounds on the complex shear
modulus in three dimensions",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "453",
number = "1964",
pages = "1849--1880",
year = "1997",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Milton:1998:MCP,
author = "G. W. Milton and A. B. Movchan",
title = "Mapping certain planar elasticity problems to
antiplane ones",
journal = j-EUR-J-MECH-A-SOLIDS,
volume = "17",
number = "1",
pages = "1--11",
year = "1998",
CODEN = "EJASEV",
ISSN = "0997-7538",
fjournal = "European Journal of Mechanics. A. Solids",
}
@Article{Milton:1999:BCN,
author = "G. W. Milton and S. K. Serkov",
title = "Bounding the current in nonlinear conducting
composites",
journal = j-APPL-MECH-REV,
year = "1999",
CODEN = "AMREAD",
ISSN = "0003-6900",
note = "submitted",
}
@Article{Milton:1999:OCB,
author = "G. W. Milton and V. Nesi",
title = "Optimal {G}-closure bounds via stability under
lamination",
journal = j-ARCH-RAT-MECH-ANAL,
year = "1999",
CODEN = "AVRMAW",
ISSN = "0003-9527",
note = "in print",
}
@Book{Milton:2000:EPC,
author = "G. W. Milton",
title = "Effective properties of composites",
publisher = pub-CUP,
address = pub-CUP:adr,
year = "2000",
note = "in preparation",
}
@Book{Moreau:1988:TNM,
editor = "J.-J. Moreau and P. D. Panagiotopoulos and G. Strang",
title = "Topics in nonsmooth mechanics",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xiv + 329",
year = "1988",
ISBN = "3-7643-1907-0",
MRnumber = "MR89c:00054",
}
@Article{Morrey:1943:MIP,
author = "C. B. Morrey",
title = "Multiple integral problems in the calculus of
variations and related topics",
journal = "Univ. of California Publ. Math. (N. S.)",
volume = "1",
pages = "1--130",
year = "1943",
MRclass = "49.0X",
MRnumber = "6,180b",
}
@Article{Morrey:1952:QLS,
author = "C. B. Morrey",
title = "Quasi-convexity and the lower semicontinuity of
multiple integrals",
journal = "Pacific Journal of Mathematics",
volume = "2",
pages = "25--53",
year = "1952",
}
@Book{Morrey:1966:MIC,
author = "C. B. Morrey",
title = "Multiple integrals in the calculus of variations",
publisher = pub-SV,
address = "New York",
pages = "ix + 506",
year = "1966",
note = "Die Grundlehren der mathematischen Wissenschaften,
Band 130.",
}
@Article{Movchan:1992:ICE,
author = "A. B. Movchan",
title = "Integral characteristics of elastic inclusions and
cavities in the two-dimensional theory of elasticity",
journal = j-EUR-J-APPL-MATH,
volume = "3",
number = "",
pages = "21--30",
year = "1992",
ISSN = "0956-7925",
}
@Book{Movchan:1995:MMS,
author = "A. B. Movchan and N. V. Movchan",
title = "Mathematical modelling of solids with nonregular
boundaries",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xiv + 325",
year = "1995",
ISBN = "0-8493-8338-2",
}
@InCollection{Muller:1996:ART,
author = "Stefan M{\"u}ller and V. {\v{S}}ver{\'a}k",
booktitle = "Geometric analysis and the calculus of variations",
title = "Attainment results for the two-well problem by convex
integration",
publisher = "Internat. Press",
address = "Cambridge, MA",
pages = "239--251",
year = "1996",
}
@TechReport{Muller:1998:QLS,
author = "S. M{\"u}ller and I. Fonseca",
title = "A-quasiconvexity, lower semicontinuity and {Young}
measures",
type = "Preprint",
institution = "Max-Planck-Institut f{\"u}r Mathematik in der
Naturwissenshaften",
address = "Leipzig, Germany",
year = "1998",
}
@Article{Murat:1972:TNE,
author = "F. Murat",
title = "Th{\'e}or{\`e}mes de non-existence pour des
probl{\`e}mes de contr{\^o}le dans les coefficients",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "274",
pages = "A395--A398",
year = "1972",
CODEN = "CHASAP",
ISSN = "0151-0509",
}
@Article{Murat:1977:CEP,
author = "F. Murat",
title = "Contre-examples pour divers probl{\`e}mes o{\`u} le
contr{\^o}le intervient dans les coefficients",
journal = j-ANN-MAT-PURA-APPL-4,
pages = "49--68",
year = "1977",
CODEN = "ANLMAE",
ISSN = "0373-3114",
fjournal = "Annali di Matematica Pura ed Applicata. Serie Quarta",
}
@Article{Murat:1981:CPC,
author = "F. Murat",
title = "Compacit{\'e} par compensation: condition
n{\'e}cessaire et suffisante de continuit{\'e} faible
sous une hypoth{\`e}se de rang constant",
journal = j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
volume = "8",
number = "1",
pages = "69--102",
year = "1981",
CODEN = "PSNAAI",
ISSN = "0391-173X",
fjournal = "Annali della Scuola Normale Superiore di Pisa. Classe
di Scienze. Serie IV",
}
@Article{Murat:1985:CVH,
author = "F. Murat and L. Tartar",
title = "Calcul des variations et homog{\'e}n{\'e}isation",
volume = "57",
publisher = pub-EYROLLES,
address = pub-EYROLLES:adr,
pages = "319--369",
year = "1985",
note = "English translation as \cite{Murat:1997:CVH}",
series = "Collection de la Direction des {\'E}tudes et
Recherches d'Electricit{\'e} de France",
}
@InCollection{Murat:1985:MHT,
author = "F. Murat and L. Tartar",
booktitle = "Les m{\'e}thodes de l'homog{\'e}n{\'e}isation:
th{\'e}orie et applications en physique ({English}:
Homogenization methods: theory and applications in
physics ({Br{\'e}au-sans-Nappe}, 1983))",
publisher = "????",
address = "????",
pages = "??--??",
year = "1985",
}
@InCollection{Murat:1985:OCH,
author = "F. Murat and L. Tartar",
booktitle = "Nonlinear variational problems (Isola d'Elba, 1983)",
title = "Optimality conditions and homogenization",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "1--8",
year = "1985",
}
@Article{Murat:1991:HRS,
author = "F. Murat",
title = "Homogenization of renormalized solutions of elliptic
equations",
journal = j-ANN-INST-HENRI-POINCARE-ANAL-NON-LINEAIRE,
volume = "8",
number = "3-4",
pages = "309--332",
year = "1991",
ISSN = "0294-1449",
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Analyse Non
Lin{\'e}aire",
}
@TechReport{Murat:1993:SRE,
author = "F. Murat",
title = "Soluciones renormalizadas de {EDP} elipticas no
lineales (in {Spanish})",
number = "R 93023",
institution = "Publications du Laboratoire d'Analyse Num{\'e}rique,
Universit{\'e} Pierre et Marie Curie",
year = "1993",
abstract = "This paper consists of the notes of a series of
lectures I gave at the University of Seville in May
1992. The problem under consideration is $- div (A \
grad \ u) - div(\phi(u)) + \lambda u = f \ \mbox{in}
\Omega, u = 0 \ \mbox{on} \ \partial \Omega$, where $A$
is a coercive matrix with coefficients in $L^\infty
(\Omega), \phi : R \longrightarrow R^N$ is a locally
Lipschitz continuous function (no growth condition on
$\phi$ is assumed), $\lambda$ is strictly positive and
$f$ belongs to $L^1(\Omega)$. The definition of
renormalized solution of this problem is introduced.
The renormalized solution is proved to exist and to be
unique.",
}
@Article{Murat:1994:PMC,
author = "F. Murat and A. Sili",
fullauthor = "F. Murat and Ali Sili",
title = "Probl{\`e}mes monotones dans des cylindres de faible
diam{\`e}tre",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "319",
number = "6",
pages = "567--572",
year = "1994",
CODEN = "CASMEI",
ISSN = "0764-4442",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences.
S{\'e}rie I. Math{\'e}matique",
}
@Article{Murat:1995:PMC,
author = "F. Murat and A. Sili",
fullauthor = "F. Murat and Ali Sili",
title = "Probl{\`e}mes monotones dans des cylindres de faible
diam{\`e}tre form{\'e}s de mat{\'e}riaux
h{\'e}t{\'e}rog{\`e}nes",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "320",
number = "10",
pages = "1199--1204",
year = "1995",
CODEN = "CASMEI",
ISSN = "0764-4442",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences.
S{\'e}rie I. Math{\'e}matique",
}
@InCollection{Murat:1997:C,
author = "F. Murat and L. Tartar",
booktitle = "Topics in the mathematical modelling of composite
materials",
title = "${H}$-convergence",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "21--43",
year = "1997",
}
@InCollection{Murat:1997:CVH,
author = "F. Murat and L. Tartar",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modeling of composite
materials",
title = "Calculus of variations and homogenization",
volume = "31",
publisher = "Birkh{\"a}user",
address = "Boston",
pages = "139--173",
year = "1997",
note = "Translation. The original publication in
\cite{Murat:1985:CVH}",
series = "Progress in nonlinear differential equations and their
applications",
}
@TechReport{Murat:19xx:EUR,
author = "F. F. Murat",
title = "Existence and Uniqueness of Renormalized Solutions of
Elliptic Equations",
institution = "????",
address = "????",
year = "19xx",
}
@Book{Muskhelishvili:1943:SBP,
author = "N. I. Muskhelishvili",
title = "Some basic problems of the mathematical theory of
elasticity",
publisher = "Noordhoff",
address = "Groningen",
pages = "",
year = "1943",
}
@Book{Muskhelishvili:1953:SBP,
author = "N. I. Muskhelishvili",
title = "Some basic problems of the mathematical theory of
elasticity",
publisher = "P. Noordhoff Ltd.",
address = "Groningen-Holland",
year = "1953",
}
@InCollection{Neittaanmaki:1993:CFE,
author = "P. Neittaanm{\"a}ki and S. Repin and V. Rivkind",
booktitle = "Jyv{\"a}skyl{\"a}--St.\ Petersburg Seminar on Partial
Differential Equations and Numerical Methods",
title = "Conforming finite element methods using discontinuous
approximations",
publisher = "Univ. Jyv{\"a}skyl{\"a}",
address = "Jyv{\"a}skyl{\"a}",
pages = "63--87",
year = "1993",
MRnumber = "MR94g:65059",
}
@Article{Neittaanmaki:1994:DFE,
author = "P. Neittaanm{\"a}ki and S. Repin and V. Rivkind",
title = "Discontinuous finite element approximations for
functionals with linear growth",
journal = j-EW-J-NUM-MATH,
volume = "2",
number = "3",
pages = "211--228",
year = "1994",
CODEN = "EJNMEA",
ISSN = "0928-0200",
MRnumber = "MR95i:65160",
fjournal = "East-West Journal of Numerical Mathematics",
}
@Book{Nemat-Nasser:1993:MOP,
author = "S. {Nemat-Nasser} and M. Hori",
title = "Micromechanics: {Overall} properties of heterogeneous
materials",
publisher = pub-NH,
address = pub-NH:adr,
year = "1993",
}
@Article{Nesi:1991:MII,
author = "V. Nesi",
title = "Multiphase interchange inequalities",
journal = j-J-MATH-PHYS,
volume = "32",
number = "8",
pages = "2263--2275",
year = "1991",
CODEN = "JMAPAQ",
ISSN = "0022-2488",
fjournal = "Journal of Mathematical Physics",
}
@Article{Nesi:1991:PCM,
author = "V. Nesi and G. W. Milton",
title = "Polycrystalline configurations that maximize
electrical resistivity",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "39",
number = "4",
pages = "525--542",
year = "1991",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Article{Nesi:1993:CPP,
author = "V. Nesi",
title = "On the ${G}$-closure in the polycrystalline problem",
journal = j-SIAM-J-APPL-MATH,
volume = "53",
number = "1",
pages = "96--127",
year = "1993",
CODEN = "SMJMAP",
ISSN = "0036-1399",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Nesi:1993:UQC,
author = "V. Nesi",
title = "Using quasi-convex functionals to bound the effective
conductivity of composite materials",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "123A",
number = "4",
pages = "633--680",
year = "1993",
CODEN = "PREAAY",
ISSN = "0308-2105",
}
@Article{Nesi:1993:UQF,
author = "V. Nesi",
title = "Using quasiconvex functionals to bound the effective
conductivity of composite materials",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "123",
number = "4",
pages = "633--679",
year = "1993",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Nesi:1995:BEC,
author = "V. Nesi",
title = "Bounds on the effective conductivity of
two-dimensional composites made of $n\geq 3$ isotropic
phases in prescribed volume fraction: the weighted
translation method",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "125",
number = "6",
pages = "1219--1239",
year = "1995",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Nesi:1997:HCQ,
author = "V. Nesi",
title = "Homogenized coefficients, quasiregular mappings and
higher integrability of the gradients in
two-dimensional conductivity",
journal = j-CALC-VAR-PARTIAL-DIFFER-EQU,
volume = "5",
number = "1",
pages = "21--36",
year = "1997",
ISSN = "0944-2669",
fjournal = "Calculus of Variations and Partial Differential
Equations",
}
@Book{Neuman:1980:TGE,
author = "J. von Neumann and O. Morgenstern",
title = "Theory of games and economic behavior",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
edition = "third",
pages = "xx + 641",
year = "1980",
ISBN = "0-691-00362-9",
}
@Article{Nevard:1997:HRB,
author = "J. Nevard and J. B. Keller",
title = "Homogenization of rough boundaries and interfaces",
journal = j-SIAM-J-APPL-MATH,
volume = "57",
number = "6",
pages = "1660--1686",
year = "1997",
CODEN = "SMJMAP",
ISSN = "0036-1399",
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Niordson:1997:ODV,
author = "F. Niordson",
fullauthor = "Frithiof Niordson",
title = "Optimal disks in vibration",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "34",
number = "23",
pages = "2957--2968",
year = "1997",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Norris:1985:DSE,
author = "A. N. Norris",
title = "A differential scheme for the effective moduli of
composites",
journal = j-MECH-MATER,
volume = "4",
pages = "1--16",
year = "1985",
CODEN = "MSMSD3",
ISSN = "0167-6636",
}
@Article{Norris:1999:SIR,
author = "A. N. Norris",
title = "Stress invariance and redundant moduli in
three-dimensional elasticity",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
year = "1999",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
note = "In print",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Book{Nowacki:1986:TAE,
author = "W. Nowacki",
title = "Theory of asymmetric elasticity",
publisher = "Pergamon Press",
address = "Oxford",
pages = "viii + 383",
year = "1986",
ISBN = "0-08-027584-2",
note = "Translated from the Polish by H. Zorski.",
}
@Article{Oleinik:1995:SNH,
author = "O. A. Ole{\u\i}nik and G. A. Yosifian and R. Temam",
title = "Some nonlinear homogenization problems",
journal = j-APPLIC-ANAL,
volume = "57",
number = "1-2",
pages = "101--118",
year = "1995",
CODEN = "APANCC",
ISSN = "0003-6811",
MRnumber = "MR97d:35015",
fjournal = "Applicable Analysis. An International Journal",
}
@Article{Olhoff:1974:ODV,
author = "N. Olhoff",
title = "Optimal design of vibrating rectangular plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "10",
pages = "93--109",
year = "1974",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Olhoff:1977:BOL,
author = "N. Olhoff and S. H. Rasmussen",
title = "On bimodal optimum loads of clamped columns",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "13",
number = "",
pages = "605--514",
year = "1977",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Olhoff:1979:OSR,
author = "N. Olhoff and J. E. Taylor",
title = "On optimal structural remodeling",
journal = j-J-OPT-THEORY-APPL,
volume = "27",
number = "4",
pages = "571--582",
year = "1979",
CODEN = "JOTABN",
ISSN = "0022-3239",
fjournal = "Journal of Optimization Theory and Applications",
}
@Article{Olhoff:1981:ICO,
author = "N. Olhoff and K.-T. Cheng",
title = "An investigation concerning optimal design of solid
elastic plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "17",
pages = "305--321",
year = "1981",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Olhoff:1981:SRA,
author = "N. Olhoff and K. A. Lurie and A. Cherkaev and A. V.
Fedorov",
title = "Sliding Regimes and Anisotropy in Optimal Design of
Vibrating Axisymmetric Plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "17",
number = "10",
pages = "931--948",
year = "1981",
CODEN = "IJSOAD",
ISSN = "0020-7683",
MRclass = "73K40 (49B22 73K12)",
MRnumber = "82f:73035",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Solids and Structures",
xxtitle = "Sliding regimes and anisotropy in optimal design of
vibrating axisymmetric plates",
}
@Article{Olhoff:1983:SO,
author = "N. Olhoff and J. E. Taylor",
title = "On structural optimization",
journal = j-J-APPL-MECH,
volume = "50",
number = "4",
pages = "1139--1151",
year = "1983",
CODEN = "JAMCAV",
ISSN = "0021-8936",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Series E. Journal of Applied Mechanics",
}
@Article{Olhoff:1991:CIS,
author = "N. Olhoff and M. P. Bend\-s{\o}e and J. Rasmussen",
title = "On {CAD-integrated} Structural Topology and Design
Optimization",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "89",
number = "",
pages = "259--279",
year = "1991",
CODEN = "CMMECC",
ISSN = "0045-7825",
}
@InCollection{Olhoff:1992:CIS,
author = "N. Olhoff and M. P. Bend\-s{\o}e and J. Rasmussen",
booktitle = "Shape and layout optimization of structural systems
and optimality criteria methods",
title = "{CAD-integrated} structural topology and design
optimization",
publisher = pub-SV,
address = "Vienna",
pages = "171--197",
year = "1992",
}
@InProceedings{Olhoff:1993:TOB,
author = "N. Olhoff and J. Thomsen and J. Rasmussen",
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials",
title = "Topology Optimization of Bi-Material Structures",
organization = "",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "191--206",
month = "",
year = "1993",
}
@Article{Olhoff:1998:TOT,
author = "N. Olhoff and J. Scheel and E. R{\o}nholt",
title = "Topology optimization of three-dimensional structures
using optimum microstructures",
journal = j-STRUCT-OPTIM,
volume = "16",
pages = "1--18",
year = "1998",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Panasenko:1982:PSA,
author = "G. P. Panasenko",
title = "The principle of splitting of an averaged operator for
a non-linear system of equations in periodic and random
skeletal structures",
journal = j-SOVIET-MATH-DOKL,
volume = "25",
number = "2",
pages = "290--295",
year = "1982",
ISSN = "0197-6788",
}
@Article{Panasenko:1993:ASE,
author = "G. P. Panasenko",
title = "Asymptotic solutions of the elasticity theory system
of equations for lattice and skeletal structures",
journal = j-MAT-SB,
volume = "75",
number = "1",
pages = "85--110",
year = "1993",
ISSN = "1064-5616",
}
@TechReport{Panasenko:1994:HLL,
author = "G. P. Panasenko",
title = "Homogenization of lattice-like domains:
{L-convergence}",
type = "Report",
number = "CNRS URA 740, 178",
institution = "Equipe d'Analyse Num{\'e}rique",
address = "Lyon/Saint-Etienne",
year = "1994",
}
@Book{Papalambros:1988:POD,
author = "P. Y. Papalambros and D. J. Wilde",
title = "Principles of optimal design",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "xxii + 416",
year = "1988",
ISBN = "0-521-30674-4",
note = "Modeling and computation",
}
@InCollection{Papanicolaou:1982:BVP,
author = "G. Papanicolaou and S. Varadhan",
editor = "",
booktitle = "Colloquia Mathematica Societatis J{\'a}nos Bolyai 27,
Random Fields (Esztergom, Hungary 1979)",
title = "Boundary value problems with rapidly oscillating
coefficients",
publisher = pub-NH,
address = pub-NH:adr,
pages = "835--873",
year = "1982",
}
@Article{Parry:1995:PRO,
author = "G. P. Parry",
title = "On the planar rank-one convexity condition",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "125",
number = "2",
pages = "247--264",
year = "1995",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Book{Parton:1984:MMTa,
author = "V. Z. Parton and P. I. Perlin",
title = "Mathematical methods of the theory of elasticity.
{Vol}. 1",
publisher = "``Mir''",
address = "Moscow",
pages = "317",
year = "1984",
note = "Translated from the Russian by Ram S. Wadhwa",
}
@Book{Parton:1984:MMTb,
author = "V. Z. Parton and P. I. Perlin",
title = "Mathematical methods of the theory of elasticity.
{Vol}. 2",
publisher = "``Mir''",
address = "Moscow",
pages = "356",
year = "1984",
note = "Translated from the Russian by Ram S. Wadhwa",
}
@Article{Pasa:1989:BEC,
author = "G. I. Pa{\c{s}}a",
title = "Bounds for effective coefficients of periodic
fiber-reinforced materials",
journal = j-SIAM-J-MATH-ANA,
volume = "20",
number = "1",
pages = "106--115",
year = "1989",
CODEN = "SJMAAH",
ISSN = "0036-1410",
}
@Article{Pedersen:1989:OOO,
author = "P. Pedersen",
title = "On Optimal Orientation of Orthotropic Materials",
journal = j-STRUCT-OPTIM,
volume = "1",
number = "",
pages = "101--106",
year = "1989",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Pedersen:1990:BEE,
author = "P. Pedersen",
title = "Bounds on Elastic Energy in Solids of Orthotropic
Materials",
journal = j-STRUCT-OPTIM,
volume = "2",
number = "",
pages = "55--63",
year = "1990",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Pedersen:1991:TOD,
author = "P. Pedersen",
title = "On Thickness and Orientational Design with Orthotropic
Materials",
journal = j-STRUCT-OPTIM,
volume = "3",
number = "",
pages = "69--78",
year = "1991",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@InProceedings{Pedersen:1993:ODB,
author = "P. Pedersen and J. E. Taylor",
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials",
title = "Optimal Design Based on Power-Law Non-Linear
Elasticity",
organization = "",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "51--66",
month = "",
year = "1993",
}
@Article{Pedregal:1989:WCW,
author = "P. Pedregal",
title = "Weak continuity and weak lower semicontinuity for some
compensation operators",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "113",
number = "3-4",
pages = "267--279",
year = "1989",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@Book{Pedregal:1997:PMV,
author = "P. Pedregal",
title = "Parametrized measures and variational principles",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xii + 212",
year = "1997",
ISBN = "3-7643-5697-9",
}
@Article{Pedregal:1998:NQR,
author = "P. Pedregal and V. {\v{S}}ver{\'a}k",
title = "A note on quasiconvexity and rank-one convexity for
$2\times 2$ matrices",
journal = j-J-CONVEX-ANAL,
volume = "5",
number = "1",
pages = "107--117",
year = "1998",
ISSN = "0944-6532",
fjournal = "Journal of Convex Analysis",
}
@Article{Petersson:1998:SCT,
author = "J. Petersson and O. Sigmund",
title = "Slope constrained topology optimization",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "41",
number = "8",
pages = "1417--1434",
year = "1998",
CODEN = "IJNMBH",
ISSN = "0029-5981",
MRnumber = "MR1623194",
fjournal = "International Journal for Numerical Methods in
Engineering",
}
@Article{Petukhov:1977:OCP,
author = "L. V. Petukhov",
title = "Optimal control of processes described by equations of
hyperbolic type",
journal = j-PRIKL-MAT-MEH,
volume = "41",
number = "3",
pages = "387--398",
year = "1977",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR58:2521",
fjournal = "Prikl. Mat. Meh.",
}
@Article{Petukhov:1984:ADM,
author = "L. V. Petukhov and S. I. Repin",
title = "Application of duality methods in problems of
optimizing the shape of elastic bodies",
journal = j-PRIKL-MAT-MEH,
volume = "48",
number = "5",
pages = "830--838",
year = "1984",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR87d:73058",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Petukhov:1986:ECM,
author = "L. V. Petukhov",
title = "Elastic constructions of minimal volume satisfying
strength requirements",
journal = j-DOKL-AKAD-NAUK,
volume = "287",
number = "6",
pages = "1350--1353",
year = "1986",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRnumber = "MR87g:73067",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Petukhov:1986:OPT,
author = "L. V. Petukhov",
title = "On optimal problems of the theory of elasticity with
unknown boundaries",
journal = j-PRIKL-MAT-MEH,
volume = "50",
number = "2",
pages = "231--236",
year = "1986",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR88e:73020",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Petukhov:1989:OER,
author = "L. V. Petukhov",
title = "Optimal elastic regions of maximum rigidity",
journal = j-PRIKL-MAT-MEH,
volume = "53",
number = "1",
pages = "88--95",
year = "1989",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR90e:73093",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Petukhov:1990:NES,
author = "L. V. Petukhov and K. E. Sokov",
title = "Nonhomogeneous elastic structures that are optimal
with respect to stiffness",
journal = j-PRIKL-MAT-MEH,
volume = "54",
number = "2",
pages = "275--280",
year = "1990",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR91j:73049",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Petukhov:1992:DEP,
author = "L. V. Petukhov",
title = "Dual estimates in problems on the design of elastic
structures",
journal = j-PRIKL-MAT-MEH,
volume = "56",
number = "3",
pages = "434--441",
year = "1992",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR93j:73059",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Prikladnaya Matematika
i Mekhanika",
}
@Article{Petukhov:1995:NWC,
author = "L. V. Petukhov",
title = "Necessary {Weierstrass} conditions for elliptic
systems",
journal = j-PRIKL-MAT-MEH,
volume = "59",
number = "5",
pages = "742--749",
year = "1995",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR96k:49045",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Prikladnaya Matematika
i Mekhanika",
}
@Article{Phan-Thien:1983:NTO,
author = "N. Phan-Thien and G. W. Milton",
title = "New third-order bounds on the effective moduli of
${N}$-phase composites",
journal = j-QUART-APPL-MATH,
volume = "41",
number = "1",
pages = "59--74",
year = "1983/84",
CODEN = "QAMAAY",
ISSN = "0033-569X",
fjournal = "Quarterly of Applied Mathematics",
}
@Book{Pinch:1993:OCC,
author = "Enid R. Pinch",
title = "Optimal control and the calculus of variations",
publisher = pub-CLARENDON-PRESS,
address = pub-CLARENDON-PRESS:adr,
pages = "viii + 234",
year = "1993",
ISBN = "0-19-853217-2",
}
@Article{Pineau:1976:IUS,
author = "A. Pineau",
title = "Influence of uniaxial stress on the morphology of
coherent precipitates during coarsening --- elastic
energy considerations",
journal = j-ACTA-METALL,
volume = "24",
pages = "559--564",
year = "1976",
CODEN = "AMETAR",
ISSN = "0001-6160",
}
@Book{Pironneau:1984:OSD,
author = "O. Pironneau",
title = "Optimal Shape Design for Elliptic Systems",
publisher = pub-SV,
address = "",
pages = "",
year = "1984",
}
@Book{Polya:1951:IIM,
author = "G. P{\'o}lya and G. Szeg{\"o}",
title = "Isoperimetric {Inequalities} in {Mathematical}
{Physics}",
volume = "27",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xvi + 279",
year = "1951",
series = "Annals of Mathematics Studies",
}
@Book{Pontryagin:1964:MTO,
author = "L. S. Pontryagin and V. G. Boltyanskii and R. V.
Gamkrelidze and E. F. Mishchenko",
title = "The mathematical theory of optimal processes",
publisher = "A Pergamon Press Book. The Macmillan Co., New York",
pages = "vii + 338",
year = "1964",
note = "Translated by D. E. Brown.",
}
@Book{Pontryagin:1986:SW,
author = "L. S. Pontryagin and V. G. Boltyanski{\u\i} and R. V.
Gamkrelidze and E. F. Mishchenko",
title = "Selected works. {Vol}. 4",
publisher = "Gordon \& Breach Science Publishers",
address = "New York",
pages = "xxiv + 360",
year = "1986",
ISBN = "2-88124-134-4",
note = "The mathematical theory of optimal processes. Edited
and with a preface by R. V. Gamkrelidze. Translated
from the Russian by K. N. Trirogoff. Translation edited
by L. W. Neustadt, with a preface by L. W. Neustadt and
K. N. Trirogoff. Reprint of the 1962 English
translation.",
}
@Book{Prager:1961:IMC,
author = "W. Prager",
title = "Introduction to mechanics of continua",
publisher = "Ginn and Co.",
address = "Boston, MA; Toronto; London",
pages = "x + 230",
year = "1961",
series = "Introductions to Higher Mathematics",
}
@Article{Prager:1968:OCS,
author = "W. Prager",
title = "Optimality Criteria in Structural Design",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "61",
number = "3",
pages = "794--796",
year = "1968",
CODEN = "PNASA6",
ISSN = "0027-8424",
}
@Book{Prager:1974:ISO,
author = "W. Prager",
title = "Introduction to structural optimization",
publisher = pub-SV,
address = "Vienna",
pages = "iv + 80",
year = "1974",
note = "Course held at the Department of Mechanics of Solids,
International Centre for Mechanical Sciences, Udine,
October, 1974, International Centre for Mechanical
Sciences, Courses and Lectures, No. 212.",
}
@InProceedings{Prager:1977:OSG,
author = "W. Prager and G. Rozvany",
editor = "A. Bednarek and L. Cesari",
booktitle = "Dynamical systems",
title = "Optimization of structural geometry",
publisher = pub-AP,
address = pub-AP:adr,
pages = "265--294",
year = "1977",
}
@Article{Raitum:1977:NEC,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Necessary extremum conditions for a certain class of
problems on the optimization of plane-parallel magnetic
fields",
journal = j-LATV-MAT-EZEG,
volume = "21",
pages = "69--89, 235",
year = "1977",
ISSN = "0321-2270, 0458-8223",
oldvolume = "Vyp. 21",
}
@Article{Raitum:1978:EEP,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Extension of extremal problems connected with linear
elliptic equations",
journal = j-DOKL-AKAD-NAUK,
volume = "243",
number = "2",
pages = "281--283",
year = "1978",
CODEN = "DANKAS",
ISSN = "0002-3264",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Raitum:1979:OCP,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On optimal control problems for linear elliptic
equations",
journal = j-DOKL-AKAD-NAUK,
volume = "244",
number = "4",
pages = "828--830",
year = "1979",
CODEN = "DANKAS",
ISSN = "0002-3264",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Raitum:1980:CSS,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Closure in ${L}\sb2$\ of the set of solutions of a
family of nonlinear elliptic equations",
journal = j-DIFFER-URAVN-MINSK-1965,
volume = "16",
number = "3",
pages = "501--506, 574",
year = "1980",
ISSN = "0374-0641",
fjournal = "Differentsial\cprime nye Uravneniya",
}
@Article{Raitum:1980:SCW,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Sufficient conditions for weak sequential closedness
of the set of solutions of linear elliptic equations",
journal = j-LATV-MAT-EZEG,
number = "24",
pages = "142--155, 260",
year = "1980",
ISSN = "0321-2270",
fjournal = "Latvi\u \i ski\u \i \ Gosudarstvenny\u \i \
Universitet imeni P. Stuchki. Latvi\u \i ski\u \i \
Matematicheski\u \i \ Ezhegodnik",
}
@Article{Raitum:1981:CQE,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On ${G}$-convergence of quasilinear elliptic operators
with unbounded coefficients",
journal = j-DOKL-AKAD-NAUK,
volume = "261",
number = "1",
pages = "30--34",
year = "1981",
CODEN = "DANKAS",
ISSN = "0002-3264",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Raitum:1981:EPL,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Extremal properties of laminar structures",
journal = j-OPTIMIZATION,
volume = "12",
number = "4",
pages = "563--573",
year = "1981",
CODEN = "OPTZDQ",
ISSN = "0323-3898",
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
}
@Article{Raitum:1981:SCN,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Some consequences of necessary conditions for an
extremum in optimal control problems for elliptic
equations",
journal = j-LATV-MAT-EZEG,
number = "25",
pages = "71--80, 247",
year = "1981",
ISSN = "0321-2270",
fjournal = "Latvi\u \i ski\u \i \ Gosudarstvenny\u \i \
Universitet imeni P. Stuchki. Latvi\u \i ski\u \i \
Matematicheski\u \i \ Ezhegodnik",
}
@Article{Raitum:1982:CAL,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On the ${G}$-convergence of almost linear elliptic
operators with unbounded lower coefficients",
journal = j-LATV-MAT-EZEG,
volume = "26",
pages = "101--113, 281",
year = "1982",
ISSN = "0321-2270",
fjournal = "Latvi\u \i ski\u \i \ Gosudarstvenny\u \i \
Universitet imeni P. Stuchki. Latvi\u \i ski\u \i \
Matematicheski\u \i \ Ezhegodnik",
}
@Article{Raitum:1982:NEC,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Necessary extremum conditions in problems of optimal
control for a nonlinear elliptic equation",
journal = j-SIB-MAT-Z,
volume = "23",
number = "1",
pages = "144--152, 222",
year = "1982",
ISSN = "0037-4474",
fjournal = "Akademiya Nauk SSSR. Sibirskoe Otdelenie. Sibirski\u
\i \ Matematicheski\u \i \ Zhurnal",
}
@Article{Raitum:1983:QES,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Questions of the existence of a solution in problems
of optimal control of leading coefficients of linear
elliptic equations",
journal = j-DIFFER-URAVN-MINSK-1965,
volume = "19",
number = "6",
pages = "1040--1047",
year = "1983",
ISSN = "0374-0641",
fjournal = "Differentsial\cprime nye Uravneniya",
}
@Article{Raitum:1984:EEP,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On the extension of extremal problems connected with
semilinear elliptic equations",
journal = j-LATV-MAT-EZEG,
number = "28",
pages = "104--115",
year = "1984",
ISSN = "0321-2270",
fjournal = "Latvi\u\i ski\u\i\ Gosudarstvenny\u\i\ Universitet
imeni P. Stuchki. Latvi\u\i ski\u\i\
Matematicheski\u\i\ Ezhegodnik",
}
@Article{Raitum:1984:NOCa,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Necessary optimality conditions for systems described
by nonlinear elliptic equations. {I}",
journal = j-Z-ANAL-ANWEND,
volume = "3",
number = "1",
pages = "65--79",
year = "1984",
ISSN = "0232-2064",
fjournal = "Zeitschrift f{\"u}r Analysis und Ihre Anwendungen",
}
@Article{Raitum:1984:NOCb,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Necessary optimality conditions for systems described
by nonlinear elliptic equations. {II}",
journal = j-Z-ANAL-ANWEND,
volume = "3",
number = "2",
pages = "133--152",
year = "1984",
ISSN = "0232-2064",
fjournal = "Zeitschrift f{\"u}r Analysis und Ihre Anwendungen",
}
@Article{Raitum:1985:GNC,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On a generalization of the notion of ${G}$-convergence
for quasilinear elliptic systems of equations",
journal = j-LATV-MAT-EZEG,
number = "29",
pages = "73--83, 251",
year = "1985",
ISSN = "0321-2270",
fjournal = "Latvi\u\i ski\u\i\ Gosudarstvenny\u\i\ Universitet
imeni P. Stuchki. Latvi\u\i ski\u\i\
Matematicheski\u\i\ Ezhegodnik",
}
@Article{Raitum:1985:PCH,
author = "U. {\"E}. Ra{\u\i}tum",
title = "The passage to the convex hull of a set of admissible
operators in optimal control problems",
journal = j-DOKL-AKAD-NAUK,
volume = "285",
number = "2",
pages = "289--292",
year = "1985",
CODEN = "DANKAS",
ISSN = "0002-3264",
fjournal = "Doklady Akademii Nauk SSSR",
}
@InCollection{Raitum:1987:PPC,
author = "U. {\"E}. Ra{\u\i}tum",
booktitle = "Topological structures and their mappings (Russian)",
title = "Preservation of potentiality in the case of
${G}$-convergence of monotone operators",
publisher = "Latv. Gos. Univ.",
address = "Riga",
pages = "102--105, v",
year = "1987",
}
@Article{Raitum:1988:CFE,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On the construction of formal extensions of optimal
control problems for elliptic equations",
journal = j-LATV-MAT-EZEG,
number = "32",
pages = "28--36, 239--240",
year = "1988",
ISSN = "0321-2270",
fjournal = "Latvi\u\i ski\u\i\ Gosudarstvenny\u\i\ Universitet
imeni P. Stuchki. Latvi\u\i ski\u\i\
Matematicheski\u\i\ Ezhegodnik",
}
@Book{Raitum:1989:OCP,
author = "U. {\"E}. Ra{\u\i}tum",
title = "Optimal control problems for elliptic equations",
publisher = "``Zinatne''",
address = "Riga",
pages = "278",
year = "1989",
ISBN = "5-7966-0165-2",
note = "In Russian",
}
@TechReport{Raitums:1999:LRC,
author = "U. {\"E}. Ra{\u\i}tum",
title = "On the local representation of ${G}$-closure",
number = "206",
institution = "Department of mathematics, University of
{Jyv\"{a}skyl\"{a}}",
address = "{Jyv\"{a}skyl\"{a}}, Finland",
month = mar,
year = "1999",
ISSN = "0780-8569",
}
@Article{Repin:1987:MCN,
author = "S. I. Repin",
title = "Minimization of a class of nondifferentiable
functionals by means of the relaxation method",
journal = j-Z-VYCISL-MAT-MAT-FIZ,
volume = "27",
number = "7",
pages = "976--983, 1117",
year = "1987",
CODEN = "ZVMFAN",
ISSN = "0044-4669",
MRnumber = "MR89a:90113",
fjournal = "Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime
no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki",
}
@Article{Repin:1991:VFDa,
author = "S. I. Repin",
title = "Variational formulations for discontinuous
displacement fields in problems of ideal plasticity",
journal = j-DOKL-AKAD-NAUK,
volume = "320",
number = "6",
pages = "1340--1344",
year = "1991",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRnumber = "MR93d:73040",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Repin:1991:VFDb,
author = "S. I. Repin",
title = "Variational formulations for discontinuous
displacement fields in problems of the deformation
theory of plasticity without hardening",
journal = j-PRIKL-MAT-MEH,
volume = "55",
number = "6",
pages = "1026--1034",
year = "1991",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR93d:73039",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Repin:1994:ASV,
author = "S. I. Repin",
title = "On the approximation of solutions of variational
problems in the theory of ideal plasticity",
journal = j-IZV-VYSS-UCEBN-ZAVED-MAT,
number = "9",
pages = "60--69",
year = "1994",
CODEN = "IVUMBY",
ISSN = "0021-3446",
MRnumber = "MR96h:73025",
fjournal = "Izvestiya Vysshikh Uchebnykh Zavedeni\u\i.
Matematika",
}
@Article{Repin:1994:NAN,
author = "S. I. Repin",
title = "Numerical analysis of nonsmooth variational problems
of perfect plasticity",
journal = j-RUSS-J-NUM-ANAL-MATH-MODEL,
volume = "9",
number = "1",
pages = "61--74",
year = "1994",
CODEN = "RJNMEH",
ISSN = "0927-6467",
MRnumber = "MR95c:65188",
fjournal = "Russian Journal of Numerical Analysis and Mathematical
Modelling",
}
@Article{Repin:1994:SPM,
author = "S. I. Repin",
title = "Solutions of problems in the mathematical theory of
plasticity that contain discontinuities in the
displacement fields",
journal = j-PRIKL-MAT-MEH,
volume = "58",
number = "1",
pages = "142--152",
year = "1994",
CODEN = "PMAMAF",
ISSN = "0032-8235",
MRnumber = "MR95h:73044",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Prikladnaya Matematika
i Mekhanika",
}
@Article{Repin:1995:EES,
author = "S. Repin and G. Ser{\"e}gin",
title = "Error estimates for stresses in the finite element
analysis of the two-dimensional elasto-plastic
problems",
journal = j-INT-J-ENG-SCI,
volume = "33",
number = "2",
pages = "255--268",
year = "1995",
CODEN = "IJESAN",
ISSN = "0020-7225",
MRnumber = "MR96c:73068",
fjournal = "International Journal of Engineering Science",
}
@InCollection{Repin:1995:EWS,
author = "S. Repin and G. Ser{\"e}gin",
booktitle = "Nonlinear evolution equations",
title = "Existence of a weak solution of the minimax problem
arising in {Coulomb-Mohr} plasticity",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "189--220",
year = "1995",
MRnumber = "MR96b:73116",
}
@Article{Repin:1995:PEC,
author = "S. I. Repin",
title = "A priori estimates for the convergence of
variational-difference methods in problems of ideal
plasticity",
journal = j-ZAP-NAUC-SEMIN-LENINGR-OTD-ORDENA,
volume = "221",
number = "Kraev. Zadachi Mat. Fiz. i Smezh. Voprosy Teor.
Funktsii. 26",
pages = "226--234, 260",
year = "1995",
CODEN = "ZNSLAF",
ISSN = "0373-2703",
MRnumber = "MR97c:73029",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Sankt-Peterburgskoe
Otdelenie. Matematicheski\u\i\ Institut im. V. A.
Steklova. Zapiski Nauchnykh Seminarov (POMI)",
}
@Article{Reshetnyak:1967:GTS,
author = "Y. G. Reshetnyak",
title = "General theorems on semi-continuity and quasiconvexity
of functionals",
journal = j-SIB-MAT-Z,
volume = "8",
pages = "801--816",
year = "1967",
ISSN = "0037-4474",
}
@Article{Reshetnyak:1967:LTC,
author = "Y. G. Reshetnyak",
title = "{Liouville}'s theorem on conformal mappings under
minimal regularity assumptions",
journal = j-SIB-MAT-Z,
volume = "8",
pages = "69--85",
year = "1967",
ISSN = "0037-4474",
}
@Article{Reuss:1929:BFV,
author = "A. Reuss",
title = "{Berechnung der Fliessgrenze von Mischkristallen auf
Grund Plastizit{\"a}tsbedingung f{\"u}r Einkristalle}",
journal = j-Z-ANGE-MATH-MECH,
volume = "9",
number = "1",
pages = "49--58",
year = "1929",
CODEN = "ZAMMAX",
ISSN = "0044-2267",
}
@Article{Rockafellar:1966:EFD,
author = "R. Rockafellar",
title = "Extension of {Fenchel}'s duality theorem for convex
functions",
journal = j-DUKE-MATH,
volume = "33",
pages = "81--89",
year = "1966",
CODEN = "DUMJAO",
ISSN = "0012-7094",
}
@Article{Rockafellar:1967:DSE,
author = "R. Rockafellar",
title = "Duality and stability in extremum problems involving
convex functions",
journal = j-PAC-J-MATH,
volume = "21",
pages = "167--187",
year = "1967",
CODEN = "PJMAAI",
ISSN = "0030-8730",
}
@Book{Rockafellar:1997:CA,
author = "R. Rockafellar",
title = "Convex analysis",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xviii + 451",
year = "1997",
ISBN = "0-691-01586-4",
note = "Reprint of the 1970 original, Princeton Paperbacks.",
}
@Article{Rodrigues:1999:DMP,
author = "H. C. Rodrigues and C. A. Soto and J. E. Taylor",
title = "A design model to predict optimal two-material
composite structure",
journal = j-STRUCT-OPTIM,
volume = "17",
pages = "186--198",
year = "1999",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Roitburd:1969:DSC,
author = "A. L. Roitburd",
title = "The domain structure of crystals formed in the solid
phase",
journal = j-SOV-PHYS-SOLID-STATE,
volume = "10",
pages = "2870--2876",
year = "1969",
CODEN = "SPSSA7",
ISSN = "0038-5654",
}
@Article{Rosakis:1994:RBP,
author = "P. Rosakis and H. C. Simpson",
title = "On the relation between polyconvexity and rank-one
convexity in nonlinear elasticity",
journal = j-J-ELAST,
volume = "37",
number = "2",
pages = "113--137",
year = "1994/95",
CODEN = "JELSAY",
ISSN = "0374-3535",
fjournal = "Journal of Elasticity",
}
@Article{Rosen:1970:ETE,
author = "B. W. Rosen and Z. Hashin",
title = "Effective thermal expansion coefficients and specific
heats of composite materials",
journal = j-INT-J-ENG-SCI,
volume = "8",
pages = "157--173",
year = "1970",
CODEN = "IJESAN",
ISSN = "0020-7225",
}
@Article{Rozonoer:1959:PMP,
author = "L. I. Rozono{\`e}r",
title = "{L. S. Pontryagin} maximum principle in the theory of
optimum systems. {I}, {II}, {III}",
journal = j-AUTOMATIC-REMOTE-CTL,
volume = "20",
pages = "1288--1302, 1405--1421, 1517--1532",
year = "1959",
ISSN = "0538-7361",
}
@Article{Rozvany:1982:SPP,
author = "G. I. N. Rozvany and N. Olhoff and Keng Tung Cheng and
J. E. Taylor",
title = "On the Solid Plate Paradox in Structural
Optimization",
journal = j-J-STRUCT-MECH,
volume = "10",
number = "1",
pages = "1--32",
year = "1982",
CODEN = "JSMHA2",
ISSN = "0360-1218",
fjournal = "Journal of Structural Mechanics",
}
@Article{Rozvany:1987:LWD,
author = "G. I. N. Rozvany and N. Olhoff and M. P. Bend\-s{\o}e
and others",
title = "Least Weight Design of Perforated Elastic Plates",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "23",
number = "",
pages = "521--536 (part {I}) and 537--550 (part {II})",
year = "1987",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Book{Rozvany:1989:SDO,
author = "G. I. N. Rozvany",
title = "Structural design via optimality criteria",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xxvi + 463",
year = "1989",
ISBN = "90-247-3613-7",
note = "The Prager approach to structural optimization",
}
@Article{Rozvany:1993:EOS,
author = "G. I. N. Rozvany and O. Sigmund and T. Lewi{\'n}ski
and D. Gerdes and T. Birker",
title = "Exact optimal structural layouts for non-self-adjoint
problems",
journal = j-STRUCT-OPTIM,
volume = "5",
pages = "204--206",
year = "1993",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Rozvany:1993:OTT,
author = "G. I. N. Rozvany and T. Lewi{\'n}ski and O. Sigmund
and D. Gerdes and T. Birker",
title = "Optimal topology of trusses or perforated deep beams
with rotational restraints at both ends",
journal = j-STRUCT-OPTIM,
volume = "5",
pages = "268--270",
year = "1993",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Rozvany:1995:LOS,
author = "G. I. N. Rozvany and M. P. Bend\-s{\o}e and U.
Kirsch",
title = "Layout Optimization of Structures",
journal = j-APPL-MECH-REV,
volume = "48",
number = "2",
pages = "41--119",
year = "1995",
CODEN = "AMREAD",
ISSN = "0003-6900",
}
@Book{Rozvany:1997:TOS,
editor = "G. I. N. Rozvany",
title = "Topology optimization in structural mechanics",
publisher = pub-SV,
address = "Vienna",
pages = "viii + 322",
year = "1997",
ISBN = "3-211-82907-5",
}
@Book{Rubichek:1997:ROT,
author = "T. Roub{\'\i}{\v{c}}ek",
title = "Relaxation in optimization theory and variational
calculus",
publisher = "Walter de Gruyter \& Co.",
address = "Berlin",
pages = "xiv + 474",
year = "1997",
ISBN = "3-11-014542-1",
}
@Article{Rubinstein:1987:LBP,
author = "J. Rubinstein and J. B. Keller",
title = "Lower bounds on permeability",
journal = j-PHYS-FLUIDS,
volume = "30",
pages = "2919--2921",
year = "1987",
CODEN = "PHFLE6",
ISSN = "1070-6631",
}
@Article{Rubinstein:1988:DCR,
author = "J. Rubinstein and S. Torquato",
title = "Diffusion controlled reactions: Mathematical
formulations, variational principles, and rigorous
bounds",
journal = j-J-CHEM-PHYS,
volume = "88",
pages = "6372--6380",
year = "1988",
CODEN = "JCPSA6",
ISSN = "0021-9606",
}
@PhdThesis{Rudelson:1989:PTS,
author = "M. Rudelson",
title = "Phase transitions in solids",
school = "St. Petersburg Technical University",
address = "St. Petersburg, Russia",
year = "1989",
}
@Book{Rund:1966:HJT,
author = "H. Rund",
fullauthor = "Hanno Rund",
title = "The {Hamilton-Jacobi} theory in the calculus of
variations: {Its} role in mathematics and physics",
publisher = "D. Van Nostrand Co., Ltd.",
address = "London; Toronto; New York",
pages = "xi + 404",
year = "1966",
}
@Article{Rykhlevskii:1988:STF,
author = "Ya. Rykhlevski{\u\i}",
title = "Symmetry of tensor functions and a spectral theorem",
journal = j-USP-MEH,
volume = "11",
number = "3",
pages = "77--125",
year = "1988",
CODEN = "0137-3722",
ISSN = "0137-3722",
fjournal = "Advances in Mechanics",
}
@Article{Ryzhik:1996:TEE,
author = "L. Ryzhik and G. Papanicolaou and J. Keller",
title = "Transport equations for elastic and other waves in
random media",
journal = j-WAVE-MOTION,
volume = "24",
number = "4",
pages = "327--370",
year = "1996",
CODEN = "WAMOD9",
ISSN = "0165-2125",
fjournal = "Wave Motion. An International Journal Reporting
Research on Wave Phenomena",
}
@Book{Saada:1993:ETA,
author = "Adel S. Saada",
title = "Elasticity theory and applications",
publisher = "Robert E. Krieger Publishing Co. Inc.",
address = "Malabar, FL",
edition = "Second",
pages = "xxii + 775",
year = "1993",
ISBN = "0-89464-561-7",
}
@Book{Sagan:1992:ICV,
author = "H. Sagan",
fullauthor = "Hans Sagan",
title = "Introduction to the calculus of variations",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 449",
year = "1992",
ISBN = "0-486-67366-9",
note = "Corrected reprint of the 1969 original.",
}
@Article{Sage:1999:MSS,
author = "D. S. Sage",
title = "Multiplication of subrepresentations for simply
reducible groups and vanishing of {Racah}
coefficients",
journal = "??",
volume = "??",
number = "??",
pages = "??--??",
month = "??",
year = "1999",
note = "In preparation.",
}
@Article{Sali:1997:EMA,
author = "L. Sali and D. J. Bergman",
fullauthor = "Leora Sali and D. J. Bergman",
title = "Effective medium approximation for strongly nonlinear
media",
journal = j-J-STAT-PHYS,
volume = "86",
number = "3-4",
pages = "455--479",
year = "1997",
CODEN = "JSTPSB",
ISSN = "0022-4715",
MRnumber = "MR98a:73008",
fjournal = "Journal of Statistical Physics",
}
@Book{Sanches-Palensiya:1984:CNS,
author = "E. {S{\'a}nchez-Palencia}",
title = "{\cyr {Neodnorodnye} sredy i teoriya kolebani\u\i }",
publisher = pub-MIR,
address = pub-MIR:adr,
pages = "472",
year = "1984",
note = "Translated from the English by V. V. Zhikov,
Translation edited and with a preface by O. A.
Ole{\u\i}nik, With an appendix by L. Tartar.",
}
@Book{Sanchez-Palencia:1980:NMV,
author = "E. {S{\'a}nchez-Palencia}",
title = "Nonhomogeneous media and vibration theory",
publisher = pub-SV,
address = "Berlin",
pages = "ix + 398",
year = "1980",
ISBN = "3-540-10000-8",
}
@Book{Save:1985:SOV,
author = "M. Save and W. Prager and G. Sacchi",
title = "Structural optimization. {Vol}. 1",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "xii + 334",
year = "1985",
ISBN = "0-306-41861-4",
note = "Optimality criteria.",
}
@Book{Savin:1961:SCH,
author = "G. N. Savin",
title = "Stress concentration around holes",
publisher = "Pergamon Press",
address = "New York",
year = "1961",
}
@Article{Sawicz:1995:BCP,
author = "R. Sawicz and K. Golden",
title = "Bounds on the complex permittivity of matrix-particle
composites",
journal = j-J-APPL-PHYS,
volume = "78",
pages = "7240--7246",
year = "1995",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@InCollection{Schnack:1992:SOF,
author = "E. Schnack and U. Sp{\"o}rl and G. Iancu",
booktitle = "Shape and Layout Optimization of Structural Systems
and Optimality Criteria Methods",
title = "{2D}- and {3D}-Shape Optimization with {FEM} and
{BEM}",
chapter = "22",
publisher = pub-SV,
address = "",
pages = "457--482",
year = "1992",
}
@Article{Schulgasser:1976:RBS,
author = "K. Schulgasser",
title = "Relationship between single-crystal and polycrystal
electrical conductivity",
journal = j-J-APPL-PHYS,
volume = "47",
pages = "1880--1886",
year = "1976",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@Article{Schulgasser:1977:BCS,
author = "K. Schulgasser",
title = "Bounds on the conductivity of statistically isotropic
polycrystals",
journal = j-J-PHYS-C,
volume = "10",
pages = "407--417",
year = "1977",
CODEN = "JPSOAW",
ISSN = "0022-3719",
}
@Article{Schulgasser:1989:TEP,
author = "K. Schulgasser",
title = "Thermal expansion of polycrystals",
journal = j-J-MATER-SCI-LETT,
volume = "8",
pages = "228--229",
year = "1989",
CODEN = "JMSLD5, JMTSAS",
ISSN = "0261-8028",
}
@Article{Seyranian:1987:MEO,
author = "A. P. Seyranian",
title = "Multiple Eigenvalues in Optimization Problems",
journal = j-PRIKL-MAT-MEH,
volume = "51",
number = "",
pages = "272--275",
year = "1987",
CODEN = "AMMEEQ",
ISSN = "0253-4827",
}
@Article{Seyranian:1994:MES,
author = "A. P. Seyranian and E. Lund and N. Olhoff",
title = "Multiple Eigenvalues in Structural Optimization
Problems",
journal = j-STRUCT-OPTIM,
volume = "8",
number = "4",
pages = "207--227",
year = "1994",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Book{Shilov:1996:EFA,
author = "Georgi E. Shilov",
title = "Elementary functional analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "viii + 334",
year = "1996",
ISBN = "0-486-68923-9",
note = "Revised English edition translated from the Russian
and edited by Richard A. Silverman, Corrected reprint
of the 1974 English translation.",
}
@Article{Sigmund:1988:NIT,
author = "O. Sigmund and J. Petersson",
title = "Numerical instabilities in topology optimization: {A}
survey on procedures dealing with checkerboards,
mesh-dependencies and local minima",
journal = j-STRUCT-OPTIM,
volume = "16",
pages = "68--75",
year = "1998",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
note = "A review",
}
@Article{Sigmund:1994:MPC,
author = "O. Sigmund",
title = "Materials with prescribed constitutive parameters: an
inverse homogenization problem",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "31",
number = "17",
pages = "2313--2329",
year = "1994",
CODEN = "IJSOAD",
ISSN = "0020-7683",
MRnumber = "MR95d:73005",
fjournal = "International Journal of Solids and Structures",
}
@InCollection{Sigmund:1996:SIP,
author = "O. Sigmund",
booktitle = "IUTAM Symposium on Optimization of Mechanical Systems
(Stuttgart, 1995)",
title = "Some inverse problems in topology design of materials
and mechanisms",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "277--284",
year = "1996",
MRnumber = "MR1383362",
}
@Article{Sigmund:1997:DCM,
author = "O. Sigmund",
title = "On the design of compliant mechanisms using topology
optimization",
journal = "Mechanics of Structures and Machines",
volume = "25",
number = "4",
pages = "495--526",
month = nov,
year = "1997",
}
@Article{Sigmund:1997:DME,
author = "O. Sigmund and S. Torquato",
title = "Design of materials with extreme thermal expansion
using a three-phase topology optimization method",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "6",
pages = "1037--1067",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR98i:73042",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@TechReport{Sigmund:1998:NCE,
author = "O. Sigmund",
title = "A new class of extremal composites",
type = "Report",
number = "599",
institution = "DCAMM",
address = "Technical University of Denmark",
year = "1998",
}
@Book{Silhavy:1997:MTC,
author = "M. {\v{S}}ilhav{\'y}",
title = "The mechanics and thermodynamics of continuous media",
publisher = pub-SV,
address = "Berlin",
pages = "xiv + 504",
year = "1997",
ISBN = "3-540-58378-5",
}
@Article{Silhavy:1998:PDR,
author = "M. {\v{S}}ilhav{\'y}",
title = "Polar decomposition of rank $1$ perturbations in two
dimensions",
journal = j-MATH-MECH-SOLIDS,
volume = "3",
number = "1",
pages = "107--112",
year = "1998",
CODEN = "MMESFP",
ISSN = "1081-2865",
fjournal = "Mathematics and Mechanics of Solids",
}
@Article{Sivaloganathan:1988:IRO,
author = "J. Sivaloganathan",
title = "Implications of rank one convexity",
journal = j-ANN-INST-HENRI-POINCARE-ANAL-NON-LINEAIRE,
volume = "5",
number = "2",
pages = "99--118",
year = "1988",
ISSN = "0294-1449",
fjournal = "Annales de l'Institut Henri Poincar\'e. Analyse Non
Lin\'eaire",
}
@Article{Skripnik:1990:AND,
author = "I. W. Skripnik",
title = "Averaging of Nonlinear {Dirichlet} Problems in the
Domains with Channels (in {Russian})",
journal = j-DOKL-AKAD-NAUK,
volume = "315",
number = "4",
pages = "??--??",
month = "??",
year = "1990",
CODEN = "DANKAS",
ISSN = "0002-3264",
}
@Article{Skripnik:1992:NRC,
author = "I. W. Skripnik",
title = "Necessary Regularity Condition of a Boundary Point for
a Quasi-linear Parabolic Equation (in {Russian})",
journal = "Rossiiskaja Akademja Nauk (Russian Academy of
Sciences), Matematitscheskii Sbornik (Mathematical
Collection)",
volume = "183",
number = "7",
pages = "??--??",
month = "??",
year = "1992",
}
@TechReport{Skrypnik:1994:HND,
author = "Igor V. Skrypnik",
title = "Homogenization of Nonlinear {Dirichlet} Problems in
Perforated Domains of General Structure",
number = "196/94/M",
institution = "S.I.S.S.A. ISAS",
address = "Trieste, Italy",
month = dec,
year = "1994",
abstract = "We consider a sequence of boundary value problems for
nonlinear elliptic equations in divergence form in
domains $\Omega_s \subset \Omega \subset {\bf R^n}, s =
1,2, \ldots$. Our hypothesis about the structure of the
sets $\Omega_s$ is the following: there exists a
sequence $r_s$ tending to zero such that the inequality
$C_m(K(x_0,r) \setminus \Omega_s) f \le Ar^n$ is valid
for every $x_0 \in \Omega$ and every $r \ge r_s$, where
$C_m$ is the $m-$capacity, $m$ is related to the growth
conditions of the operators associated with the
differential equations, and $K(x_0, r)$ denotes the
cube with centre $x_0$ and edge $2r$. We study tyhe
strong convergence in $L_p, p < m$ of the derivatives
of $u_s(x)$ and construct a boundary value problem
satisfied by the limit function. We construct also a
corrector for the approximation of $u_s(x)$ in
$W_{m}^{1}$. All our results are based on the
asymptotic expansion of the sequence $u_s(x)$ and on a
pointwise estimate of the solutions of a model
nonlinear boundary value problem.",
}
@Article{Smereka:1991:BFR,
author = "P. Smereka and G. W. Milton",
fullauthor = "Peter Smereka and G. W. Milton",
title = "Bubbly flow and its relation to conduction in
composites",
journal = j-J-FLUID-MECH,
volume = "233",
pages = "65--81",
year = "1991",
CODEN = "JFLSA7",
ISSN = "0022-1120",
fjournal = "Journal of Fluid Mechanics",
}
@Article{Smyshlyaev:1999:RTW,
author = "V. P. Smyshlyaev and J. R. Willis",
title = "On the relaxation of a three-well energy",
journal = "R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci.",
volume = "455",
number = "1983",
pages = "779--814",
year = "1999",
ISSN = "1364-5021",
MRclass = "74G65 (74B20 74M25)",
MRnumber = "1 701 019",
MRreviewer = "Pablo Pedregal",
bibdate = "Tue Mar 7 16:36:01 2000",
fjournal = "The Royal Society of London. Proceedings. Series A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Socrate:1993:NDE,
author = "S. Socrate and D. M. Parks",
title = "Numerical determination of the elastic driving force
for directional coarsening in {Ni-superalloys}",
journal = j-ACTA-METALL-MATER,
volume = "41",
pages = "2185--2209",
year = "1993",
CODEN = "AMATEB",
ISSN = "0956-7151",
}
@Book{Sokolnikoff:1983:MTE,
author = "I. S. Sokolnikoff",
title = "Mathematical theory of elasticity",
publisher = "Robert E. Krieger Publishing Co. Inc.",
address = "Melbourne, Fla.",
edition = "second",
pages = "xi + 476",
year = "1983",
ISBN = "0-89874-555-1",
}
@Book{Sokolowski:1992:ISO,
author = "J. Sokolowski and J.-P. Zolesio",
title = "Introduction to Shape Optimization. Shape Sensitivity
Analysis.",
publisher = pub-SV,
address = "",
pages = "",
year = "1992",
}
@InProceedings{Soto:1993:LPS,
author = "C. A. Soto and A. R. D{\'\i}az",
editor = "?. Gilmore and others",
booktitle = "Advances in Design Automatization",
title = "Layout of Plate Structures for Improved Dynamic
Responce using a Homogenization Method",
publisher = "ASME",
address = "Albuquerque, NM",
pages = "667--674",
month = "",
year = "1993",
}
@InProceedings{Soto:1993:MLO,
author = "C. A. Soto and A. R. D{\'\i}az",
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials, {Lyngby,
Denmark}",
title = "A Model for Layout Optimization of Plate Structures",
organization = "",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "337--350",
month = "",
year = "1993",
}
@Article{Soto:1993:MRP,
author = "C. A. Soto and A. R. D{\'\i}az",
title = "On Modelling of Ribbed Plates for Shape Optimization",
journal = j-STRUCT-OPTIM,
volume = "6",
number = "",
pages = "175--188",
year = "1993",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@InProceedings{Soto:1993:OLP,
author = "C. A. Soto and A. R. D{\'\i}az",
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "Topology Design of Structures, {Sesimbra, Portugal}",
title = "Optimum Layout of Plate Structures using
Homogenization",
organization = "NATO ASI",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "407--420",
month = "",
year = "1993",
}
@Article{Sternberg:1958:WUC,
author = "E. Sternberg and W. T. Koiter",
title = "The wedge under a concentrated couple: a paradox in
the two-dimensional theory of elasticity",
journal = j-J-APPL-MECH,
volume = "",
number = "December",
pages = "575--581",
year = "1958",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@Article{Straley:1976:CPR,
author = "J. P. Straley",
title = "Critical phenomena in resistor networks",
journal = j-J-PHYS-C,
volume = "9",
pages = "783--795",
year = "1976",
CODEN = "JPSOAW",
ISSN = "0022-3719",
}
@Article{Straley:1981:TPI,
author = "J. P. Straley",
title = "Thermoelectric properties of inhomogeneous materials",
journal = j-J-PHYS-D,
volume = "14",
pages = "2101--2105",
year = "1981",
CODEN = "JPAPBE",
ISSN = "0022-3727",
}
@Book{Strang:1973:AFE,
author = "G. Strang and G. J. Fix",
title = "An analysis of the finite element method",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 306",
year = "1973",
MRnumber = "MR56:1747",
note = "Prentice-Hall Series in Automatic Computation.",
}
@Book{Strang:1976:LAA,
author = "G. Strang",
title = "Linear algebra and its applications",
publisher = "Academic Press [Harcourt Brace Jovanovich
Publishers]",
address = "New York",
pages = "xi + 374",
year = "1976",
MRnumber = "MR52:5695",
}
@Book{Strang:1980:LAA,
author = "G. Strang",
title = "Linear algebra and its applications",
publisher = "Academic Press [Harcourt Brace Jovanovich
Publishers]",
address = "New York",
edition = "Second",
pages = "xi + 414",
year = "1980",
ISBN = "0-12-673660-X",
MRnumber = "MR81f:15003",
}
@Book{Strang:1986:IAM,
author = "G. Strang",
title = "Introduction to applied mathematics",
publisher = pub-WCP,
address = pub-WCP:adr,
pages = "xii + 758",
year = "1986",
ISBN = "0-9614088-0-4",
MRnumber = "MR88a:00006",
}
@InProceedings{Strang:1988:ODT,
author = "G. Strang and R. V. Kohn",
editor = "J. Moreau and others",
booktitle = "Topics in Nonsmooth Mechanics",
title = "Optimal design of a two-way conductor",
publisher = "Birkh{\"a}user",
pages = "143--155",
year = "1988",
}
@Book{Strang:1996:WFB,
author = "G. Strang and T. Nguyen",
fullauthor = "G. Strang and Truong Nguyen",
title = "Wavelets and filter banks",
publisher = pub-WCP,
address = pub-WCP:adr,
pages = "xxii + 490",
year = "1996",
ISBN = "0-9614088-7-1",
MRnumber = "MR98b:94003",
}
@Article{Suzuki:1991:HMS,
author = "K. Suzuki and N. Kikuchi",
title = "A homogenization method for shape and topology
optimization",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "93",
pages = "291--318",
year = "1991",
CODEN = "CMMECC",
ISSN = "0045-7825",
}
@InProceedings{Suzuki:1991:LOU,
author = "K. Suzuki and N. Kikuchi",
editor = "G. I. N. Rozvany",
booktitle = "Optimization of Large Structural Systems",
title = "Layout Optimization using the Homogenization Method:
Generalized Layout Design of Three-Dimensional Shells
for Car Bodies",
volume = "231",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "110--126",
month = "",
year = "1991",
ISBN = "0-7923-2128-6 (vol. 1), 0-7923-2129-4 (vol. 2)",
series = "NATO ASI series. Series E, Applied sciences",
bookpages = "xxi + 1201",
}
@TechReport{Sverak:1991:RMA,
author = "V. {\v{S}}ver{\'a}k",
title = "On regularity for the {Monge-Amp{\`e}re} equation
without convexity assumptions, preprint",
volume = "??",
number = "??",
institution = "Heriot-Watt University",
address = "Edinburgh, Scotland",
pages = "??--??",
month = "??",
year = "1991",
}
@Article{Sverak:1992:NEQ,
author = "V. {\v{S}}ver{\'a}k",
title = "New examples of quasiconvex functions",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "119",
number = "4",
pages = "293--300",
year = "1992",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Sverak:1992:ROC,
author = "V. {\v{S}}ver{\'a}k",
title = "Rank-one convexity does not imply quasiconvexity",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "120",
number = "1-2",
pages = "185--189",
year = "1992",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Sverak:1993:OSD,
author = "V. {\v{S}}ver{\'a}k",
title = "On optimal shape design",
journal = j-J-MATH-PURES-APPL,
volume = "72",
number = "6",
pages = "537--551",
year = "1993",
CODEN = "JMPAAM",
ISSN = "0021-7824",
fjournal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es.
Neuvi{\'e}me S{\'e}rie",
}
@InCollection{Sverak:1993:PTW,
author = "V. {\v{S}}ver{\'a}k",
editor = "D. Kinderlehrer and R. James and M. Luskin and J. L.
Ericksen",
booktitle = "Microstructure and phase transition",
title = "On the problem of two wells",
publisher = pub-SV,
address = "New York",
pages = "183--189",
year = "1993",
series = "IMA Vol. Math. Appl.",
}
@Article{Sverak:1993:TC,
author = "V. {\v{S}}ver{\'a}k",
title = "On {Tartar}'s conjecture",
journal = j-ANN-INST-HENRI-POINCARE-ANAL-NON-LINEAIRE,
volume = "10",
number = "4",
pages = "405--412",
year = "1993",
ISSN = "0294-1449",
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Analyse Non
Lin{\'e}aire",
}
@InProceedings{Sverak:1995:LSV,
author = "V. {\v{S}}ver{\'a}k",
booktitle = "Proceedings of the International Congress of
Mathematicians, Vol.\ 1, 2 (Z{\"u}rich, 1994)",
title = "Lower-semicontinuity of variational integrals and
compensated compactness",
publisher = "Birkh{\"a}user",
address = "Basel",
pages = "1153--1158",
year = "1995",
}
@Article{Swart:1992:EMF,
author = "P. Swart and P. Holmes",
title = "Energy minimization and the formation of
microstructure in dynamic antiplane shear",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "121",
pages = "37--85",
year = "1992",
CODEN = "AVRMAW",
ISSN = "0003-9527",
}
@Article{Talbot:1980:ESS,
author = "D. R. S. Talbot and J. R. Willis",
title = "The effective sink strength of a random array of voids
in irradiated material",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "370",
number = "1742",
pages = "351--374",
year = "1980",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Talbot:1985:VPI,
author = "D. R. S. Talbot and J. R. Willis",
title = "Variational principles for inhomogeneous nonlinear
media",
journal = j-IMA-J-APPL-MATH,
volume = "35",
number = "1",
pages = "39--54",
year = "1985",
CODEN = "IJAMDM",
ISSN = "0272-4960",
fjournal = "IMA (Institute of Mathematics and its Applications).
Journal of Applied Mathematics",
}
@Article{Talbot:1986:VAO,
author = "D. R. S. Talbot and J. R. Willis",
title = "A variational approach to the overall sink strength of
a nonlinear lossy composite medium",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "405",
number = "1828",
pages = "159--180",
year = "1986",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences",
}
@Article{Talbot:1987:BSC,
author = "D. R. S. Talbot and J. R. Willis",
title = "Bounds and self-consistent estimates for the overall
properties of nonlinear composites",
journal = j-IMA-J-APPL-MATH,
volume = "39",
number = "3",
pages = "215--240",
year = "1987",
CODEN = "IJAMDM",
ISSN = "0272-4960",
fjournal = "IMA Journal of Applied Mathematics",
}
@Article{Talbot:1990:REW,
author = "D. R. S. Talbot and J. B. Titchener and J. R. Willis",
title = "The reflection of electromagnetic waves from very
rough interfaces",
journal = j-WAVE-MOTION,
volume = "12",
number = "3",
pages = "245--260",
year = "1990",
CODEN = "WAMOD9",
ISSN = "0165-2125",
fjournal = "Wave Motion",
}
@Article{Talbot:1992:SSE,
author = "D. R. S. Talbot and J. R. Willis",
title = "Some simple explicit bounds for the overall behaviour
of nonlinear composites",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "29",
number = "14-15",
pages = "1981--1987",
year = "1992",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Talbot:1995:IHS,
author = "D. R. S. Talbot and J. R. Willis and V. Nesi",
title = "On improving the {Hashin-Shtrikman} bounds for the
effective properties of three-phase composite media",
journal = j-IMA-J-APPL-MATH,
volume = "54",
number = "1",
pages = "97--107",
year = "1995",
CODEN = "IJAMDM",
ISSN = "0272-4960",
fjournal = "IMA Journal of Applied Mathematics",
}
@InCollection{Talbot:1995:ULB,
author = "D. R. S. Talbot and J. R. Willis",
booktitle = "Anisotropy, inhomogeneity and nonlinearity in solid
mechanics (Nottingham, 1994)",
title = "Upper and lower bounds for the overall properties of a
nonlinear elastic composite",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "409--414",
year = "1995",
}
@Article{Talbot:1996:TPB,
author = "D. R. S. Talbot and J. R. Willis",
title = "Three-point bounds for the overall properties of a
nonlinear composite dielectric",
journal = j-IMA-J-APPL-MATH,
volume = "57",
number = "1",
pages = "41--52",
year = "1996",
CODEN = "IJAMDM",
ISSN = "0272-4960",
fjournal = "IMA Journal of Applied Mathematics",
}
@Article{Talbot:1997:BTO,
author = "D. R. S. Talbot and J. R. Willis",
title = "Bounds of third order for the overall response of
nonlinear composites",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "45",
number = "1",
pages = "87--111",
year = "1997",
CODEN = "JMPSA8",
ISSN = "0022-5096",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@TechReport{Tartar:1974:ER,
author = "L. Tartar",
title = "{\'E}quation de {Riccati}",
type = "S{\'e}minaire Goulaouic-Schwartz 1973--1974:
\'Equations aux d{\'e}riv{\'e}es partielles et analyse
fonctionnelle, Exp. No. 10",
institution = "Centre de Math., \'Ecole Polytech.",
address = "Paris",
pages = "11",
year = "1974",
}
@Article{Tartar:1975:PCC,
author = "L. Tartar",
booktitle = "Control theory, numerical methods and computer systems
modelling (Internat. Sympos., IRIA LABORIA,
Rocquencourt, 1974)",
title = "Probl{\`e}mes de contr{\^o}le des coefficients dans
des \'equations aux d{\'e}riv{\'e}es partielles",
volume = "107",
publisher = pub-SV,
address = "Berlin",
pages = "420--426",
year = "1975",
series = "Lecture Notes in Econom. and Math. Systems",
}
@Article{Tartar:1976:EEI,
author = "L. Tartar",
booktitle = "Dynamical systems (Proc. Internat. Sympos., Brown
Univ., Providence, RI, 1974), Vol. I",
title = "Evolution equations in infinite dimensions",
publisher = pub-AP,
address = pub-AP:adr,
pages = "167--177",
year = "1976",
}
@TechReport{Tartar:1976:EGP,
author = "L. Tartar",
title = "Existence globale pour un syst{\`e}me hyperbolique
semi lin{\'e}aire de la th{\'e}orie cin{\'e}tique des
gaz",
type = "S{\'e}minaire Goulaouic-Schwartz (1975/1976),
\'Equations aux d{\'e}riv{\'e}es partielles et analyse
fonctionnelle, Exp. No. 1",
institution = "Centre Math., \'Ecole Polytech.",
address = "Palaiseau, France",
pages = "11",
year = "1976",
}
@Article{Tartar:1977:HH,
author = "L. Tartar",
booktitle = "Singular perturbations and boundary layer theory
(Proc. Conf., \'Ecole Centrale, Lyon, 1976)",
title = "Homog{\'e}n{\'e}isation en hydrodynamique",
volume = "594",
publisher = pub-SV,
address = "Berlin",
pages = "474--481",
year = "1977",
series = "Lecture Notes in Mathematics",
}
@InCollection{Tartar:1978:EHN,
author = "L. Tartar",
booktitle = "S{\'e}minaire Goulaouic-Schwartz (1977/1978)",
title = "{\'E}quations hyperboliques non lin{\'e}aires",
publisher = "{\'E}cole Polytech.",
address = "Palaiseau, France",
year = "1978",
xxnote = "Check pages??.",
}
@InCollection{Tartar:1978:NCR,
author = "L. Tartar",
booktitle = "Contemporary developments in continuum mechanics and
partial differential equations (Proc. Internat.
Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de
Janeiro)",
title = "Nonlinear constitutive relations and homogenization",
publisher = pub-NH,
address = pub-NH:adr,
pages = "472--484",
year = "1978",
}
@InCollection{Tartar:1978:NMR,
author = "L. Tartar",
booktitle = "Journ{\'e}es d'Analyse Non Lin{\'e}aire (Proc. Conf.,
Besan\cedla con, 1977)",
title = "Une nouvelle m{\'e}thode de r{\'e}solution
d'\'equations aux d{\'e}riv{\'e}es partielles non
lin{\'e}aires",
publisher = pub-SV,
address = "Berlin",
pages = "228--241",
year = "1978",
}
@InCollection{Tartar:1978:QRS,
author = "L. Tartar",
booktitle = "\'Etude num{\'e}rique des grands syst{\`e}mes (Proc.
Sympos., Novosibirsk, 1976)",
title = "Quelques remarques sur les syst{\`e}mes
semi-lin{\'e}aires",
publisher = pub-DUNOD,
address = pub-DUNOD:adr,
pages = "198--212",
year = "1978",
}
@InCollection{Tartar:1978:SRS,
author = "L. Tartar",
booktitle = "Numerical methods in mathematical physics, geophysics
and optimal control (Sympos., Novosibirsk, 1976)
(Russian)",
title = "Some remarks on semilinear systems",
publisher = "``Nauka''\ Sibirsk. Otdel.",
address = "Novosibirsk",
pages = "84--96, 233",
year = "1978",
}
@Book{Tartar:1978:TNA,
author = "L. Tartar",
title = "Topics in nonlinear analysis",
publisher = "Universit{\'e} de Paris-Sud D{\'e}partement de
Math{\'e}matique",
address = "Orsay",
pages = "ii + 271 (not consecutively paged)",
year = "1978",
}
@InCollection{Tartar:1979:CCA,
author = "L. Tartar",
booktitle = "Nonlinear analysis and mechanics: Heriot-Watt
Symposium, Vol. IV",
title = "Compensated compactness and applications to partial
differential equations",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "136--212",
year = "1979",
}
@InCollection{Tartar:1979:ECH,
author = "L. Tartar",
booktitle = "Computing methods in applied sciences and engineering
(Proc. Third Internat. Sympos., Versailles, 1977), I,",
title = "Estimation de coefficients homog{\'e}n{\'e}is{\'e}s",
volume = "704",
publisher = pub-SV,
address = pub-SV:adr,
pages = "364--373",
year = "1979",
note = "English translation published in
\cite{Tartar:1997:EHC}.",
series = "Lecture Notes in Mathematics",
}
@InCollection{Tartar:1979:HCP,
author = "L. Tartar",
booktitle = "S{\'e}minaire Goulaouic-Schwartz (1978/1979)",
title = "Homog{\'e}n{\'e}isation et compacit{\'e} par
compensation",
publisher = "\'Ecole Polytech.",
address = "Palaiseau",
pages = "Exp. No. 9, 9",
year = "1979",
xxnote = "Check pages??.",
}
@InCollection{Tartar:1981:SOE,
author = "L. Tartar",
booktitle = "Goulaouic-Meyer-Schwartz Seminar, 1980--1981",
title = "Solutions oscillantes des \'equations de {Carleman}",
publisher = "\'Ecole Polytech.",
address = "Palaiseau",
pages = "Exp. No. XII, 15",
year = "1981",
xxnote = "Check pages??.",
}
@InCollection{Tartar:1982:SHN,
author = "L. Tartar",
booktitle = "Goulaouic-Meyer-Schwartz Seminar, 1981/1982",
title = "Syst{\`e}mes hyperboliques non lin{\'e}aires",
publisher = "\'Ecole Polytech.",
address = "Palaiseau",
pages = "Exp. No. XVIII, 13",
year = "1982",
xxnote = "Check pages??.",
}
@InCollection{Tartar:1983:CCM,
author = "L. Tartar",
booktitle = "Systems of nonlinear partial differential equations
(Oxford, 1982)",
title = "The compensated compactness method applied to systems
of conservation laws",
publisher = "Reidel",
address = "Dordrecht",
pages = "263--285",
year = "1983",
}
@InCollection{Tartar:1983:CPC,
author = "L. Tartar",
booktitle = "Nonlinear partial differential equations and their
applications. Coll{\`e}ge de France Seminar, Vol. IV
(Paris, 1981/1982)",
title = "Compacit{\'e} par compensation: r{\'e}sultats et
perspectives",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "350--369",
year = "1983",
}
@InCollection{Tartar:1984:EOE,
author = "L. Tartar",
booktitle = "Trends and applications of pure mathematics to
mechanics (Palaiseau, 1983)",
title = "{\'E}tude des oscillations dans les \'equations aux
d{\'e}riv{\'e}es partielles non lin{\'e}aires",
publisher = pub-SV,
address = "Berlin",
pages = "384--412",
year = "1984",
}
@InProceedings{Tartar:1985:EFC,
author = "L. Tartar",
editor = "P. Kree",
booktitle = "E. De Giorgi colloquium (Paris, 1983)",
title = "Estimation fines des coefficients
homog{\'e}n{\'e}is{\'e}s",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "168--187",
year = "1985",
}
@InCollection{Tartar:1986:ONP,
author = "L. Tartar",
booktitle = "Nonlinear systems of partial differential equations in
applied mathematics, Part 1 (Santa Fe, NM, 1984)",
title = "Oscillations in nonlinear partial differential
equations: compensated compactness and homogenization",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "243--266",
year = "1986",
}
@InCollection{Tartar:1986:RH,
author = "L. Tartar",
booktitle = "Homogenization and effective moduli of materials and
media (Minneapolis, Minn., 1984/1985)",
title = "Remarks on homogenization",
publisher = pub-SV,
address = "New York",
pages = "228--246",
year = "1986",
}
@InCollection{Tartar:1987:AOO,
author = "L. Tartar",
booktitle = "Nonclassical continuum mechanics (Durham, 1986)",
title = "The appearance of oscillations in optimization
problems",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "129--150",
year = "1987",
}
@InCollection{Tartar:1987:DO,
author = "Luc C. Tartar",
booktitle = "Directions in partial differential equations (Madison,
WI, 1985)",
title = "Discontinuities and oscillations",
publisher = pub-AP,
address = pub-AP:adr,
pages = "211--233",
year = "1987",
}
@Article{Tartar:1987:LEU,
author = "L. Tartar",
title = "Sur un lemme d'\'equivalence utilis{\'e} en analyse
num{\'e}rique",
journal = j-CALCOLO,
volume = "24",
number = "2",
pages = "129--140",
year = "1987",
CODEN = "CDABAE",
ISSN = "0008-0624",
fjournal = "Calcolo",
xxyear = "1988",
}
@InCollection{Tartar:1987:OAB,
author = "L. Tartar",
booktitle = "Dynamics of infinite-dimensional systems (Lisbon,
1986)",
title = "Oscillations and asymptotic behaviour for two
semilinear hyperbolic systems",
publisher = pub-SV,
address = "Berlin",
pages = "341--356",
year = "1987",
}
@InCollection{Tartar:1989:NEI,
author = "L. Tartar",
booktitle = "Partial differential equations and the calculus of
variations, Vol.\ II",
title = "Nonlocal effects induced by homogenization",
publisher = "Birkh{\"a}user Boston",
address = "Boston, MA",
pages = "925--938",
year = "1989",
}
@Article{Tartar:1990:MEH,
author = "L. Tartar",
title = "Memory effects and homogenization",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "111",
number = "2",
pages = "121--133",
year = "1990",
CODEN = "AVRMAW",
ISSN = "0003-9527",
fjournal = "Archive for Rational Mechanics and Analysis",
}
@Article{Tartar:1990:MNA,
author = "L. Tartar",
title = "${H}$-measures, a new approach for studying
homogenisation, oscillations and concentration effects
in partial differential equations",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "115",
number = "3-4",
pages = "193--230",
year = "1990",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematical and Physical Sciences",
}
@InProceedings{Tartar:1991:MA,
author = "L. Tartar",
booktitle = "Proceedings of the International Congress of
Mathematicians, Vol.\ I, II (Kyoto, 1990)",
title = "${H}$-measures and applications",
publisher = "Math. Soc. Japan",
address = "Tokyo",
pages = "1215--1223",
year = "1991",
}
@InCollection{Tartar:1991:POC,
author = "L. Tartar",
booktitle = "Ordinary and partial differential equations, Vol. III
(Dundee, 1990)",
title = "Propagation of oscillations and concentration effects
in partial differential equations",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "208--219",
year = "1991",
}
@InCollection{Tartar:1992:MTS,
author = "L. Tartar",
booktitle = "Developments in partial differential equations and
applications to mathematical physics (Ferrara, 1991)",
title = "On mathematical tools for studying partial
differential equations of continuum physics:
${H}$-measures and {Young} measures",
publisher = "Plenum",
address = "New York",
pages = "201--217",
year = "1992",
}
@InCollection{Tartar:1993:RSI,
author = "L. Tartar",
booktitle = "Boundary value problems for partial differential
equations and applications",
title = "Remarks on some interpolation spaces",
publisher = pub-MASSON,
address = pub-MASSON:adr,
pages = "229--252",
year = "1993",
}
@InCollection{Tartar:1993:SRS,
author = "L. Tartar",
editor = "D. Kinderlehrer and R. James and M. Luskin and J. L.
Ericksen",
booktitle = "Microstructure and phase transition",
title = "Some remarks on separately convex functions",
publisher = pub-SV,
address = "New York",
pages = "191--204",
year = "1993",
}
@InCollection{Tartar:1994:MA,
author = "L. Tartar",
booktitle = "Nonlinear partial differential equations and their
applications. Coll{\`e}ge de France Seminar, Vol.\ XI
(Paris, 1989--1991)",
title = "${H}$-measures and applications",
volume = "299",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "282--290",
year = "1994",
series = "Pitman Res. Notes Math. Ser.",
}
@InCollection{Tartar:1994:ROD,
author = "L. Tartar",
editor = "G. Buttazzo and G. Bouchitte and P. Suquet",
booktitle = "Calculus of variations, homogenization and continuum
mechanics",
title = "Remarks on optimal design problems",
volume = "18",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "279--296",
year = "1994",
series = "Series on advances in mathematics for applied
sciences",
}
@Article{Tartar:1995:BYM,
author = "L. Tartar",
title = "Beyond {Young} measures",
journal = j-MECCANICA-MILAN,
volume = "30",
number = "5",
pages = "505--526",
year = "1995",
CODEN = "MECCB9",
ISSN = "0025-6455",
note = "Microstructure and phase transitions in solids (Udine,
1994).",
fjournal = "Meccanica. International Journal of the Italian
Association of Theoretical and Applied Mechanics",
}
@InCollection{Tartar:1995:RHM,
author = "L. Tartar",
booktitle = "Homogenization and applications to material sciences
(Nice, 1995)",
title = "Remarks on the homogenization method in optimal design
methods",
publisher = "Gakk\=otosho",
address = "Tokyo",
pages = "393--412",
year = "1995",
}
@InCollection{Tartar:1997:EHC,
author = "L. Tartar",
editor = "A. V. Cherkaev and R. V. Kohn",
booktitle = "Topics in the mathematical modeling of composite
materials",
title = "Estimation of homogenized coefficients",
volume = "31",
publisher = "Birkh{\"a}user",
address = "Boston",
pages = "9--20",
year = "1997",
series = "Progress in nonlinear differential equations and their
applications",
}
@Article{Tartar:1997:SCA,
author = "L. Tartar and A. Yakir",
fullauthor = "L. Tartar and Arieh Yakir",
title = "Similarity classes of affine maps",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "261",
pages = "155--165",
year = "1997",
CODEN = "LAAPAW",
ISSN = "0024-3795",
fjournal = "Linear Algebra and its Applications",
}
@Article{Taylor:1984:IMM,
author = "J. E. Taylor and M. P. Bend\-s{\o}e",
title = "An interpretation for min-max structural design
problems including a method for relaxing constraints",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "20",
number = "4",
pages = "301--314",
year = "1984",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Taylor:1988:EMO,
author = "J. E. Taylor",
title = "An energy model for the optimal design of linear
continuum structures",
journal = j-STRUCT-OPTIM,
volume = "16",
pages = "116--127",
year = "1998",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Taylor:1993:GEP,
author = "J. E. Taylor",
title = "A global extremum principle for the analysis of solids
composed of softening material",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "30",
number = "15",
pages = "2057--2069",
year = "1993",
CODEN = "IJSOAD",
ISSN = "0020-7683",
fjournal = "International Journal of Solids and Structures",
}
@Article{Taylor:1994:GEP,
author = "J. E. Taylor",
title = "A global extremum principle in mixed form for
equilibrium analysis with elastic/stiffening materials
(a generalized minimum potential energy principle)",
journal = j-J-APPL-MECH,
volume = "61",
number = "4",
pages = "914--918",
year = "1994",
CODEN = "JAMCAV",
ISSN = "0021-8936",
fjournal = "American Society of Mechanical Engineers. Transactions
of the ASME. Journal of Applied Mechanics",
}
@InCollection{Taylor:1996:SMC,
author = "Jean E. Taylor",
booktitle = "Elliptic and parabolic methods in geometry
(Minneapolis, MN, 1994)",
title = "Surface motion due to crystalline surface energy
gradient flows",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "145--162",
year = "1996",
}
@InCollection{Taylor:1999:OME,
author = "J. E. Taylor",
editor = "P. Pedersen and M. P. Bend\-s{\o}e",
booktitle = "Synthesis in bio solid mechanics",
title = "Optimal modification and evolution of elastic
continuum structures",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "115--128",
year = "1999",
series = "Solid mechanics and its applications",
}
@Article{Telega:1990:HFE,
author = "J. J. Telega",
title = "Homogenization of fissured elastic solids in the
presence of unilateral conditions and friction",
journal = j-COMP-MECH,
volume = "6",
pages = "109--127",
year = "1990",
CODEN = "CMMEEE",
ISSN = "0178-7675",
}
@InCollection{Telega:1990:SRH,
author = "J. J. Telega",
editor = "M. Kleiber and J. A. Konig",
booktitle = "Inelastic Solids and Structures",
title = "Some results of homogenization in plasticity: plates
and fissured solids",
address = "Pineridge Press, Swansea",
pages = "343--260",
year = "1990",
}
@Article{Telega:1990:VMC,
author = "J. J. Telega",
title = "Variational methods and convex analysis in contact
problems and homogenization",
journal = "IFTR Reports",
volume = "38",
pages = "119--134",
year = "1990",
}
@InProceedings{Telega:1991:PHA,
author = "J. J. Telega",
editor = "G. A. Maugin",
booktitle = "Continum Models of Discrete Systems",
title = "Piezoelectricity and homogenization. Application to
biomechanics",
volume = "2",
publisher = "Longman",
address = "London",
pages = "220--229",
year = "1991",
}
@Article{Telega:1991:PPP,
author = "J. J. Telega",
title = "Perfectly plastic plates loaded by boundary bending
moments: relaxation and homogenization",
journal = j-ARCH-MECH,
volume = "43",
pages = "715--741",
year = "1991",
CODEN = "AVMHBR",
ISSN = "0373-2029",
}
@Article{Telega:1992:JRS,
author = "J. J. Telega",
title = "Justification of a refined scaling of stiffnesses of
{Reissner} plates with fine periodic structure",
journal = j-MATH-MODELS-METHODS-APPL-SCI,
volume = "3",
pages = "375--406",
year = "1992",
CODEN = "MMMSEU",
ISSN = "0218-2025",
}
@Article{Telega:1993:HEP,
author = "J. J. Telega",
title = "Homogenization and effective properties of plates
weakened by partially penetrating fissures: Convergence
and duality",
journal = j-MATH-MODEL-NUM-ANA,
volume = "27",
pages = "421--456",
year = "1993",
CODEN = "RMMAEV",
ISSN = "0764-583X",
}
@Article{Telega:1995:ELH,
author = "J. J. Telega",
title = "Epi - limit on {HB} and homogenization of
heterogeneous plastic plates",
journal = j-NONLINEAR-ANAL,
volume = "25",
pages = "499--529",
year = "1995",
CODEN = "NOANDD",
ISSN = "0362-546X",
}
@Article{Thompson:1994:ESM,
author = "M. Thompson and C. Su and P. Voorhees",
title = "The equilibrium shape of a misfitting precipitate",
journal = j-ACTA-METALL-MATER,
volume = "42",
number = "6",
pages = "2107--2122",
year = "1994",
CODEN = "AMATEB",
ISSN = "0956-7151",
}
@Article{Thomsen:1991:OCD,
author = "J. Thomsen",
title = "Optimization of Composite Disks",
journal = j-STRUCT-OPTIM,
volume = "3",
number = "",
pages = "89--98",
year = "1991",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Article{Thomsen:1992:TOS,
author = "J. Thomsen",
title = "Topology Optimization of Structures Composed of One or
Two Materials",
journal = j-STRUCT-OPTIM,
volume = "5",
number = "",
pages = "108--115",
year = "1992",
CODEN = "SOPTEQ",
ISSN = "0934-4373",
}
@Book{Timoshenko:1959:TPS,
author = "S. P. Timoshenko",
title = "Theory of Plates and Shells",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
year = "1959",
}
@Book{Timoshenko:1970:TE,
author = "S. P. Timoshenko",
title = "Theory of elasticity",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvi + 311",
year = "1970",
}
@Article{Torquato:1991:IBE,
author = "S. Torquato and J. Rubinstein",
title = "Improved bounds on the effective conductivity of
high-contrast suspensions",
journal = j-J-APPL-PHYS,
volume = "69",
pages = "7118--7125",
year = "1991",
CODEN = "JAPIAU",
ISSN = "0021-8979",
}
@InProceedings{Torquato:1999:DCR,
author = "S. Torquato",
editor = "K. Markov and L. Preziosi",
booktitle = "Heterogeneous Media: Micromechanics Modelling Methods
and Simulation",
title = "Diffusion-controlled reaction and flows in porous
media",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
year = "1999",
}
@Article{Tortorelli:1993:SAS,
author = "D. A. Tortorelli and Z. Wang",
title = "A systematic approach to shape sensitivity analysis",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "30",
number = "9",
pages = "1181--1212",
year = "1993",
CODEN = "IJSOAD",
ISSN = "0020-7683",
MRclass = "73K40 (49Q15 73V99)",
MRnumber = "94a:73033",
MRreviewer = "Vadim Komkov",
bibdate = "Tue Mar 7 16:36:10 2000",
fjournal = "International Journal of Solids and Structures",
}
@Book{Troitskii:1982:COF,
author = "V. A. Troitski{\u\i} and L. V. Petukhov",
title = "{\cyr {Optimizatsiya} formy uprugikh tel}",
publisher = "``Nauka''",
address = "Moscow",
pages = "432",
year = "1982",
MRnumber = "MR84d:73055",
}
@InCollection{Truesdell:1960:CFT,
author = "C. A. Truesdell and R. Toupin",
booktitle = "{Handbuch der Physik, Bd. III/1}",
title = "The classical field theories",
publisher = pub-SV,
address = "Berlin",
pages = "226--793; appendix, pp. 794--858",
year = "1960",
note = "With an appendix on tensor fields by J. L. Ericksen",
}
@InCollection{Truesdell:1965:NLF,
author = "C. Truesdell and W. Noll",
booktitle = "Handbuch der Physik, Band III/3",
title = "The non-linear field theories of mechanics",
publisher = pub-SV,
address = "Berlin",
pages = "1--602",
year = "1965",
}
@Book{Truesdell:1991:FCR,
author = "C. A. Truesdell",
title = "A first course in rational continuum mechanics. {Vol}.
1",
publisher = pub-AP,
address = pub-AP:adr,
edition = "Second",
pages = "xviii + 391",
year = "1991",
ISBN = "0-12-701300-8",
note = "General concepts",
}
@Article{Truskinovsky:1996:EBR,
author = "L. Truskinovsky and G. Zanzotto",
title = "Ericksen's bar revisited: energy wiggles",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "44",
number = "8",
pages = "1371--1408",
year = "1996",
CODEN = "JMPSA8",
ISSN = "0022-5096",
MRnumber = "MR97e:73015",
fjournal = "Journal of the Mechanics and Physics of Solids",
}
@Book{Tuckey:1993:NMC,
author = "C. Tuckey",
title = "Nonstandard methods in the calculus of variations",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "xiv + 94",
year = "1993",
ISBN = "0-582-23180-9",
}
@Article{Vainshtein:1997:RSR,
author = "A. Vainshtein and T. Healey and P. Rosakis and L.
Truskinovsky",
title = "The role of the spinodal region in one-dimensional
martensitic phase transitions",
journal = j-PHYSICA-D,
volume = "",
number = "",
pages = "",
year = "1997",
CODEN = "PDNPDT",
ISSN = "0167-2789",
}
@Article{vanKeulen:1997:SOA,
author = "F. {van Keulen} and A. A. Polynkine and V. V.
Toropov",
title = "Shape Optimization with Adaptive Mesh Refinement:
Target Error Selection Strategies",
journal = "Engineering Optimization",
volume = "28",
pages = "95--125",
year = "1997",
ISSN = "0305-215X",
bibdate = "Tue Mar 7 16:36:13 2000",
}
@Article{Vigdergauz:1976:IEI,
author = "S. B. Vigdergauz",
title = "Integral equation of the inverse problem of the plane
theory of elasticity",
journal = j-PRIKL-MAT-MEH,
volume = "40",
number = "3",
pages = "518--521",
year = "1976",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Vigdergauz:1977:CIP,
author = "S. B. Vigdergauz",
title = "On a case of the inverse problem of two-dimensional
theory of elasticity",
journal = j-PRIKL-MAT-MEH,
volume = "41",
number = "5",
pages = "927--933",
year = "1977",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Vigdergauz:1982:OCA,
author = "S. B. Vigdergauz",
title = "Optimality conditions in axisymmetric problems of
elasticity theory",
journal = j-PRIKL-MAT-MEH,
volume = "46",
number = "2",
pages = "210--213",
year = "1982",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Vigdergauz:1983:IPT,
author = "S. B. Vigdergauz",
title = "Inverse problem of three-dimensional elasticity",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "18",
number = "2",
pages = "83--86",
year = "1983",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@Article{Vigdergauz:1984:OCE,
author = "S. B. Vigdergauz",
title = "Optimal cavities in an elastic space with axial
symmetry",
journal = j-IZV-AKAD-ARM-SSR-MEH,
volume = "37",
number = "3",
pages = "51--58",
year = "1984",
CODEN = "IAMHAZ",
ISSN = "0002-3051",
note = "In Russian.",
}
@Article{Vigdergauz:1986:EEP,
author = "S. B. Vigdergauz",
title = "Effective elastic parameters of a plate with a regular
system of equal-strength holes",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "21",
number = "2",
pages = "165--169",
year = "1986",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@Article{Vigdergauz:1986:HPOa,
author = "S. B. Vigdergauz and A. V. Cherkaev",
title = "A hole in a plate, optimal for its biaxial
extension-compression",
journal = j-PRIKL-MAT-MEH,
volume = "50",
number = "3",
pages = "524--528",
year = "1986",
CODEN = "PMAMAF",
ISSN = "0032-8235",
fjournal = "Akademiya Nauk SSSR. Otdelenie Tekhnicheskikh Nauk.
Institut Mekhaniki. Prikladnaya Matematika i
Mekhanika",
}
@Article{Vigdergauz:1986:HPOb,
author = "S. B. Vigdergauz and A. V. Cherkaev",
title = "A hole in a plate, optimal for its biaxial
extension-compression",
journal = j-J-APPL-MATH-MECH,
volume = "50",
number = "3",
pages = "359--372",
year = "1986",
CODEN = "JAMMAR",
ISSN = "0021-8928",
MRclass = "401--404 (1987); translated from {\em Prikl. Mat.
Mekh.} {\bf 50} (1986)",
MRnumber = "88g:73073",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
}
@Article{Vigdergauz:1988:GCE,
author = "S. B. Vigdergauz",
title = "The geometrical characteristics of equally-strong
boundaries of elastic bodies",
journal = j-PRIKL-MAT-MEH,
volume = "52",
number = "3",
pages = "371--376",
year = "1988",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Vigdergauz:1988:SSE,
author = "S. B. Vigdergauz",
title = "Stressed state of an elastic plane with
constant-stress holes",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "23",
number = "3",
pages = "96--99",
year = "1988",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@Article{Vigdergauz:1989:PHP,
author = "S. B. Vigdergauz",
title = "Piecewise-homogeneous plates of extremal stiffness",
journal = j-PRIKL-MAT-MEH,
volume = "53",
number = "1",
pages = "76--80",
year = "1989",
CODEN = "PMAMAF",
ISSN = "0032-8235",
}
@Article{Vigdergauz:1989:RSE,
author = "S. B. Vigdergauz",
title = "Regular structures with extremal elastic properties",
journal = j-IZV-AKAD-NAUK-SSSR-MEH-TVERD-TELA,
volume = "24",
number = "3",
pages = "57--63",
year = "1989",
CODEN = "IZMTB9",
ISSN = "0572-3299",
}
@Article{Vigdergauz:1994:TDGa,
author = "S. B. Vigdergauz",
title = "Two-dimensional grained composites of extreme
rigidity",
journal = j-J-APPL-MECH,
volume = "61",
number = "2",
pages = "390--394",
year = "1994",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@Article{Vigdergauz:1994:TDGb,
author = "S. B. Vigdergauz",
title = "Three-dimensional grained composites of extreme
thermal properties",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "42",
number = "5",
pages = "729--740",
year = "1994",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Vigdergauz:1996:RLE,
author = "S. B. Vigdergauz",
title = "Rhombic lattice of equi-stress inclusions in an
elastic plate",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "49",
number = "4",
pages = "565--580",
year = "1996",
CODEN = "QJMMAV",
ISSN = "0033-5614",
abstract = "In this paper, we extend the equi-strength concept to
optimize the elastic behaviour of two-dimensional
grained composites in which identical foreign
inclusions form rhombic network interacting with the
principal material. The analytical solution based upon
the complex-valued potentials of Kolosov-Muskhelishvili
employs the doubly periodic Weierstrass elliptic
functions of a negative determinantto obtain,
explicitly, the parametric equations of the equi-stress
contours. To the author's best knowledge,
non-rectangular period cells have never been considered
in the literature, so this paper may be regarded as a
first attempt to advance in this direction. It is shown
that the lattice type has little influence on the
stress field in the composites, but is predominant for
the shaping of the optimal inclusions.",
ams = "33E05, 35R35, 73C02, 49Q10, 73K20, 73K40",
keywords = "grained composites, effective energy, equi-stress
boundaries, optimal structures",
}
@Book{Vinson:1987:BSC,
author = "J. R. Vinson and R. L. Sierakowski",
title = "The Behaviour of Structures Composed of Composite
Materials",
volume = "",
publisher = "M.us Nijhoff Publishers",
address = "Dordrecht, The Netherlands",
edition = "",
month = "",
year = "1987",
series = "",
}
@Book{Voigt:1928:LK,
author = "W. Voigt",
title = "{Lehrbuch der Kristallphysik}",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
year = "1928",
}
@Article{Voorhees:1992:ORT,
author = "P. W. Voorhees",
title = "Ostwald ripening of two-phase mixtures",
journal = j-ANN-REV-MATERIAL-SCI,
volume = "22",
pages = "197--215",
year = "1992",
CODEN = "ARMSCX",
ISSN = "0084-6600",
}
@InCollection{Vutsan:1983:NSO,
author = "Ya. P. Vutsan and U. {\"E}. Ra{\u\i}tum",
booktitle = "Applied problems in mathematical physics",
title = "On the numerical solution of optimal control problems
for linear elliptic equations",
publisher = "Latv. Gos. Univ.",
address = "Riga",
pages = "83--97",
year = "1983",
}
@Article{Walpole:1966:BOE,
author = "L. Walpole",
title = "On bounds for the overall elastic moduli of
inhomogeneous systems {I} and {II}",
journal = j-J-MECH-PHYS-SOLIDS,
volume = "14",
pages = "151--162, 289--301",
year = "1966",
CODEN = "JMPSA8",
ISSN = "0022-5096",
}
@Article{Wang:1984:OPD,
author = "C.-M. Wang and G. I. N. Rozvany and N. Olhoff",
title = "Optimal Plastic Design of Axisymmetric Solid Plates
with a Maximum Thickness Constraint",
journal = j-COMP-STRUCTURES,
volume = "18",
number = "4",
pages = "653--665",
year = "1984",
CODEN = "CMSTCJ",
ISSN = "0045-7949",
}
@Article{Wang:1986:OPD,
author = "C.-M. Wang and V. Thevendran and G. I. N. Rozvany and
N Olhoff",
title = "Optimal Plastic Design of Circular Plates: Numerical
Solutions and Built-In Edges",
journal = j-COMP-STRUCTURES,
volume = "22",
number = "4",
pages = "519--528",
year = "1986",
CODEN = "CMSTCJ",
ISSN = "0045-7949",
}
@Book{Warga:1972:OCD,
author = "J. Warga",
title = "Optimal control of differential and functional
equations",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xiii + 531",
year = "1972",
}
@Article{Warga:1977:SDR,
author = "J. Warga",
title = "Steepest descent with relaxed controls",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "15",
number = "4",
pages = "674--682",
year = "1977",
CODEN = "SJCODC",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
}
@Article{Warga:1991:NPC,
author = "J. Warga",
title = "Nonsmooth problems with conflicting controls",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "29",
number = "3",
pages = "678--701",
year = "1991",
CODEN = "SJCODC",
ISSN = "0363-0129",
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Control and Optimization",
}
@Article{Webman:1975:NSE,
author = "I. Webman and J. Jortner and M. H. Cohen",
title = "Numerical simulation of electrical conductivity in
microscopically inhomogeneous materials",
journal = j-PHYS-REV-B,
volume = "11",
pages = "2885--2892",
year = "1975",
CODEN = "PLRBAQ",
ISSN = "0556-2805",
}
@Book{Weinstock:1974:CV,
author = "R. Weinstock",
title = "Calculus of variations",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 326",
year = "1974",
note = "With applications to physics and engineering, Reprint
of the 1952 edition.",
}
@Book{Wells:1975:EEA,
author = "J. H. Wells and L. R. Willis",
title = "Embeddings and Extensions in Analysis",
publisher = pub-SV,
address = pub-SV:adr,
year = "1975",
}
@Article{Wheeler:1976:RCS,
author = "L. T. Wheeler",
title = "On the role of constant stress surfaces in the problem
of minimizing elastic stress concentration",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "2",
pages = "779--789",
year = "1976",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Wheeler:1982:VMS,
author = "L. T. Wheeler and I. A. Kunin",
title = "On voids of minimum stress concentration",
journal = j-INT-J-SOLIDS-STRUCT,
volume = "18",
number = "1",
pages = "85--89",
year = "1982",
CODEN = "IJSOAD",
ISSN = "0020-7683",
}
@Article{Wheeler:1992:SMF,
author = "L. T. Wheeler",
title = "Stress minimum forms for elastic solids",
journal = j-APPL-MECH-REV,
volume = "45",
number = "1",
pages = "1--11",
month = jan,
year = "1992",
CODEN = "AMREAD",
ISSN = "0003-6900",
}
@InProceedings{Wheeler:1994:IMS,
author = "L. T. Wheeler",
editor = "Y. C. Angel",
booktitle = "Anisotropy and Inhomogeneity in Elasticity and
Plasticity",
title = "Inhomogeneities of minimum stress concentration",
volume = "158",
pages = "??--??",
year = "1994",
series = "AMD Amer. Soc. Mech. Eng.",
}
@Article{Wiener:1912:AMP,
author = "W. Wiener",
title = "{Die Theorie des Mischk{\"o}rpers f{\"u}r das Feld des
stationa{\"a}ren St{\"o}rmung. Erste Abhandlung die
Mittelswerts{\"a}tze f{\"u}r Kraft, Polarization und
Energie}",
journal = "{Abhandlungen der Mathematisch Physischen Klasse der
K{\"o}niglischen-Sachsischen Gesellschaft der
Wissenschaften}",
volume = "32",
pages = "509--604",
year = "1912",
}
@Article{Willis:1952:SSR,
author = "M. L. Willis",
title = "Stress singularities resulting from various boundary
condition in angular corners of plate in extension",
journal = j-J-APPL-MECH,
volume = "19",
number = "4",
pages = "",
year = "1952",
CODEN = "JAMCAV",
ISSN = "0021-8936",
}
@InProceedings{Willis:1981:VRM,
author = "J. R. Willis",
editor = "C.-S. Yih",
booktitle = "Advances in Applied Mechanics",
title = "Variational and related methods for the overall
properties of composite materials",
volume = "21",
publisher = pub-AP,
address = pub-AP:adr,
pages = "2--78",
year = "1981",
}
@InCollection{Willis:1982:ETC,
author = "J. R. Willis",
editor = "H. G. Hopkins and M. J. Sewell",
booktitle = "Mechanics of solids",
title = "Elasticity theory of composites",
publisher = "Pergamon Press",
address = "Oxford, New York",
pages = "653--686",
year = "1982",
}
@InCollection{Willis:1990:VMT,
author = "J. R. Willis and D. R. S. Talbot",
booktitle = "Continuum models and discrete systems, Vol.\ 1 (Dijon,
1989)",
title = "Variational methods in the theory of random composite
materials",
publisher = "Longman Sci. Tech.",
address = "Harlow",
pages = "113--131",
year = "1990",
}
@Article{Wittrick:1962:RCE,
author = "W. H. Wittrick",
title = "Rates of Change of Eigenvalues, With Reference to
Buckling and Vibration Problems",
journal = j-J-R-AERONAUT-SOC,
volume = "66",
number = "",
pages = "590--591",
year = "1962",
ISSN = "0368-3931",
}
@Article{Young:1942:GSCa,
author = "L. C. Young",
title = "Generalized surfaces in the calculus of variations",
journal = j-ANN-MATH-2,
volume = "43",
pages = "84--103",
year = "1942",
CODEN = "ANMAAH",
ISSN = "0003-486X",
}
@Article{Young:1942:GSCb,
author = "L. C. Young",
title = "Generalized surfaces in the calculus of variations.
{II}",
journal = j-ANN-MATH-2,
volume = "43",
pages = "530--544",
year = "1942",
CODEN = "ANMAAH",
ISSN = "0003-486X",
}
@Book{Young:1969:LCV,
author = "L. C. Young",
title = "Lectures on the calculus of variations and optimal
control theory",
publisher = "W. B. Saunders Co.",
address = "Philadelphia",
pages = "xi + 331",
year = "1969",
note = "Foreword by Wendell H. Fleming.",
}
@Article{Yurinsky:1991:CBM,
author = "V. V. Yurinsky",
title = "Covariance Bounds for Means with respect to
Distributions of Switching Diffusions in Random
Environment",
journal = j-SIBERIAN-ADV-MATH,
volume = "1",
number = "2",
pages = "185--199",
year = "1991",
ISSN = "1055-1344",
note = "Translated from PRIM, Vol. 13, pp. 169-180, 1989.",
abstract = "The paper considers resolvents of matrix elliptic
operators in the case when these admit an explicit
probabilistic representation by a continuum integral
with respect to the distribution of a nondegenerate
diffusion in random environment. The coefficients of
the operator are assumed to satisfy a uniform strong
mixing condition. Under this restriction nontrivial
bounds are shown to exist for covariances of the
spatial averages over large blocks for random fields
solving certain second-order elliptic systems with
random coefficients. Bounds of this type are used in
evaluation of the error caused by approximation of the
solution of a well-posed boundary problem with random
highly oscillating coefficients by that of its
homogenized counterpart.",
keywords = "homogenization, averaging, random environment, random
media, diffusion, homogenization error",
}
@Article{Yurinsky:1991:HEZ,
author = "V. V. Yurinsky",
title = "On the Homogenization Error for a Zero Drift Diffusion
in a Random Medium",
journal = j-SIBERIAN-ADV-MATH,
volume = "1",
number = "4",
pages = "186--197",
year = "1991",
ISSN = "1055-1344",
note = "Translated from PRIM 20.",
abstract = "This paper studies the resolvent operator of the
generator of a nondegenerate diffusion with zero drift
in a random environment. The coefficients of the
generator are assumed to form a random field that is
homogeneous with respect to integer-valued translations
and satisfies a uniform strong mixing condition. The
main result is a bound on the covariances of a random
field obtained by applying the resolvent to a bounded
field of the above type. This bound can be used to
deduce error estimates which vanish as positive powers
of the small parameter for the homogenization
approximations to solutions of standard boundary
problems for elliptic operators of above type with
highly oscillating random coefficients. Inequalities of
this paper are derived without Cordes-type restrictions
on the span of eigenvalues of the diffusion matrix:
they are nontrivial in dimensions $d \ge 4$, while
earlier results of this kind applied to the case $d \ge
5$. The improvement is due to a new version of an
argument used to localize the dependence of the
resolvent operator on the diffusion matrix through a
decomposition of averages with respect to the
distribution of diffusion in its path space into means
over ''tubes'' of trajectories.",
keywords = "homogenization, error estimates, diffusion in random
environment, random media",
}
@Article{Zhang:1992:CQF,
author = "K. Zhang",
title = "A construction of quasiconvex functions with linear
growth at infinity",
journal = j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
volume = "19",
number = "3",
pages = "313--326",
year = "1992",
CODEN = "PSNAAI",
ISSN = "0391-173X",
fjournal = "Annali della Scuola Normale Superiore di Pisa. Classe
di Scienze. Serie IV",
}
@Article{Zhang:1997:CSR,
author = "K. Zhang",
title = "On connected subsets of ${M}\sp {2\times 2}$ without
rank-one connections",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "127",
number = "1",
pages = "207--216",
year = "1997",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Zhang:1997:NQF,
author = "K. Zhang",
title = "On non-negative quasiconvex functions with unbounded
zero sets",
journal = j-PROC-R-SOC-EDINB-SECT-A-MATH,
volume = "127",
number = "2",
pages = "411--422",
year = "1997",
CODEN = "PEAMDU",
ISSN = "0308-2105",
fjournal = "Proceedings of the Royal Society of Edinburgh. Section
A. Mathematics",
}
@Article{Zhikov:1983:CEO,
author = "V. V. Zhikov",
title = "${G}$-convergence of elliptic operators",
journal = j-MAT-ZAMETKI,
volume = "33",
number = "3",
pages = "345--356",
year = "1983",
ISSN = "0025-567X",
MRnumber = "MR85i:35049",
fjournal = "Akademiya Nauk Soyuza SSR. Matematicheskie Zametki",
}
@Article{Zhikov:1986:AFC,
author = "V. V. Zhikov",
title = "Averaging of functionals of the calculus of variations
and elasticity theory",
journal = j-IZV-AKAD-NAUK-SSSR-MAT,
volume = "50",
number = "4",
pages = "675--710, 877",
year = "1986",
CODEN = "IZAMAT",
ISSN = "0373-2436",
MRnumber = "MR88a:49026",
fjournal = "Izvestiya Akademii Nauk SSSR. Seriya
Matematicheskaya",
}
@InCollection{Zhikov:1986:DMA,
author = "V. V. Zhikov",
booktitle = "Mathematical methods in the mechanics of a deformable
solid body (Russian)",
title = "Duality methods in averaging theory",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
pages = "44--48, 166",
year = "1986",
MRnumber = "MR88f:49017",
}
@Article{Zhikov:1986:ETA,
author = "V. V. Zhikov",
title = "Estimates for the trace of an averaged matrix",
journal = j-MAT-ZAMETKI,
volume = "40",
number = "2",
pages = "226--237, 287",
year = "1986",
ISSN = "0025-567X",
MRnumber = "MR88e:35033",
fjournal = "Akademiya Nauk Soyuza SSR. Matematicheskie Zametki",
}
@Article{Zhikov:1988:ETA,
author = "V. V. Zhikov",
title = "Estimates for the trace of an averaged tensor",
journal = j-DOKL-AKAD-NAUK,
volume = "299",
number = "4",
pages = "796--800",
year = "1988",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRnumber = "MR89j:35031",
fjournal = "Doklady Akademii Nauk SSSR",
}
@Article{Zhikov:1991:EAM,
author = "V. V. Zhikov",
title = "Estimates for an averaged matrix and an averaged
tensor",
journal = j-RUSS-MATH-SURV,
volume = "46",
number = "3(279)",
pages = "49--109, 239",
year = "1991",
ISSN = "0042-1316",
fjournal = "Akademiya Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo. Uspekhi Matematicheskikh Nauk",
}
@Article{Zhikov:1991:EHM,
author = "V. V. Zhikov",
title = "Estimates for the homogenized matrix and the
homogenized tensor",
journal = j-RUSS-MATH-SURV,
volume = "46",
number = "3",
pages = "65--136",
year = "1991",
ISSN = "0036-0279",
}
@Article{Zhikov:1991:ETA,
author = "V. V. Zhikov",
title = "Estimates for the trace of an averaged tensor",
journal = j-UKR-MAT-Z,
volume = "43",
number = "6",
pages = "745--755",
year = "1991",
CODEN = "UMZHAA",
ISSN = "0041-6053",
fjournal = "Akademiya Nauk Ukrainsko\u\i\ SSR. Institut
Matematiki. Ukrainski\u \i\ Matematicheski\u\i\
Zhurnal",
}
@Article{Zhikov:1991:LEE,
author = "V. V. Zhikov",
title = "The {Lavrent{\cprime}ev} effect and averaging of
nonlinear variational problems",
journal = j-DIFFER-URAVN-MINSK-1965,
volume = "27",
number = "1",
pages = "42--50, 180",
year = "1991",
ISSN = "0374-0641",
MRnumber = "MR92j:49006",
fjournal = "Differentsial\cprime nye Uravneniya",
}
@Article{Zhikov:1992:PLN,
author = "V. V. Zhikov",
title = "Passage to the limit in nonlinear variational
problems",
journal = j-MAT-SB-MOSK,
volume = "183",
number = "8",
pages = "47--84",
year = "1992",
CODEN = "MATSAB",
ISSN = "0368-8666",
MRnumber = "MR93i:49016",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Matematicheski\u\i\
Sbornik",
}
@Book{Zhikov:1993:CUD,
author = "V. V. Zhikov and S. M. Kozlov and O. A. Ole{\u\i}nik",
title = "{\cyr {Usrednenie} differentsial\cprime nykh
operatorov}",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
pages = "464",
year = "1993",
ISBN = "5-02-014267-0",
}
@Article{Zhikov:1993:LPH,
author = "V. V. Zhikov",
title = "Lavrent{\cprime}ev phenomenon and homogenization for
some variational problems",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "316",
number = "5",
pages = "435--439",
year = "1993",
CODEN = "CASMEI",
ISSN = "0764-4442",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences.
S{\'e}rie I. Math{\'e}matique",
}
@Article{Zhikov:1995:ANV,
author = "V. V. Zhikov",
title = "On the averaging of nonlinear variational problems in
punctured domains",
journal = j-DOKL-AKAD-NAUK,
volume = "345",
number = "2",
pages = "156--160",
year = "1995",
CODEN = "DANKAS",
ISSN = "0869-5652",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@InCollection{Zhikov:1995:CHE,
author = "V. V. Zhikov",
booktitle = "Homogenization and applications to material sciences
(Nice, 1995)",
title = "Connectedness and homogenization. {Examples} of the
fractal conductivity",
publisher = "Gakk\=otosho",
address = "Tokyo",
pages = "421--430",
year = "1995",
MRnumber = "MR98h:35024",
}
@Article{Zhikov:1995:LEE,
author = "V. V. Zhikov",
title = "On the {Lavrent{\cprime}ev} effect",
journal = j-DOKL-AKAD-NAUK,
volume = "345",
number = "1",
pages = "10--14",
year = "1995",
CODEN = "DANKAS",
ISSN = "0869-5652",
MRnumber = "MR97a:49020",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@Article{Zhikov:1996:CAE,
author = "V. V. Zhikov",
title = "Connectedness and averaging. {Examples} of fractal
conductivity",
journal = j-MAT-SB-MOSK,
volume = "187",
number = "8",
pages = "3--40",
year = "1996",
CODEN = "MATSAB",
ISSN = "0368-8666",
MRnumber = "MR97h:35016",
fjournal = "Rossi\u\i skaya Akademiya Nauk. Matematicheski\u\i\
Sbornik",
}
@Article{Zhikov:1997:SVP,
author = "Vasili{\u\i} V. Zhikov",
title = "On some variational problems",
journal = j-RUSS-J-MATH-PHYS,
volume = "5",
number = "1",
pages = "105--116 (1998)",
year = "1997",
CODEN = "RJMPEL",
ISSN = "1061-9208",
MRnumber = "MR98k:49004",
fjournal = "Russian Journal of Mathematical Physics",
}
@Article{Zohdi:1996:HMH,
author = "T. I. Zohdi and J. T. Oden and G. J. Rodin",
title = "Hierarchical modeling of heterogeneous bodies",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "138",
number = "1-4",
pages = "273--298",
year = "1996",
CODEN = "CMMECC",
ISSN = "0045-7825",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
}
@Article{Zowe:1997:FMO,
author = "J. Zowe and M. Ko{\v{c}}vara and M.. Bend\-s{\o}e",
title = "Free material optimization via mathematical
programming",
journal = j-MATH-PROG,
volume = "79",
number = "1--3, Ser. B",
pages = "445--466",
year = "1997",
CODEN = "MHPGA4",
ISSN = "0025-5610",
note = "Lectures on mathematical programming (ismp97)
(Lausanne, 1997).",
fjournal = "Mathematical Programming",
xxfjournal = "Journal of the Mechanics and Physics of Solids",
}
%-----------------------------------------------------------------------
% Cross-referenced entries must come last:
@Proceedings{Ball:1988:MIC,
editor = "J. M. Ball",
booktitle = "Material instabilities in continuum mechanics: related
mathematical problems: the proceedings of a symposium
year on material instabilities in continuum mechanics",
title = "Material instabilities in continuum mechanics: related
mathematical problems: the proceedings of a symposium
year on material instabilities in continuum mechanics",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 542",
year = "1988",
ISBN = "0-19-853273-3",
LCCN = "QC176.8.P45 M381 1988",
MRclass = "73C60 (49A50 80A20 82A25)",
MRnumber = "90a:73044",
MRreviewer = "Luciano Modica",
bibdate = "Thu Oct 9 14:36:51 MDT 1997",
acknowledgement = ack-nhfb,
bookpages = "xi + 542",
xxpages = "257--268",
}
@Proceedings{Bendsoe:1992:TDS,
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "Topology Design of Structures",
title = "Topology Design of Structures",
volume = "227",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvi + 569",
year = "1992",
ISBN = "0-7923-2055-7",
LCCN = "TA658.8 .T67 1993",
series = "NATO ASI series. Series E, Applied sciences",
}
@Proceedings{Bendsoe:1993:TDS,
editor = "M. P. Bend\-s{\o}e and C. A. {Mota Soares}",
booktitle = "Topology Design of Structures: Proceedings of the NATO
Advanced Research Workshop held in Sesimbra, June
20--26, 1992",
title = "Topology Design of Structures: Proceedings of the
{NATO} Advanced Research Workshop held in Sesimbra,
June 20--26, 1992",
volume = "227",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvi + 569",
year = "1993",
ISBN = "0-7923-2055-7",
LCCN = "TA658.8.T67 1993",
series = "NATO ASI, Series E, Applied Sciences",
}
@Proceedings{Bennet:1986:OSA,
editor = "J. A. Bennet and M. E. Botkin",
title = "The Optimum Shape: Automated Structural Design",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "viii + 411",
year = "1986",
ISBN = "0-306-42419-3",
LCCN = "TA658 .G451 1985",
}
@Proceedings{Ericksen:1986:HEM,
editor = "J. L. Ericksen and D. Kinderlehrer and R. V. Kohn and
J.-L. Lions",
booktitle = "Proceedings of the IMA workshop held in Minneapolis,
Minn., October 22--26, 1984",
title = "Homogenization and effective moduli of materials and
media",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 263",
year = "1986",
ISBN = "0-387-96306-5",
MRnumber = "MR87i:73006",
}
@Proceedings{Haug:1993:CET,
editor = "E. J. Haug",
title = "Concurrent Engineering: Tools and Technologies for
Mechanical Systems Design",
volume = "108",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 998",
year = "1993",
ISBN = "0-387-56532-9 (New York), 3-540-56532-9 (Berlin)",
series = "NATO ASI series. Series F, Computer and systems
sciences",
}
@Proceedings{Joseph:1994:FEC,
editor = "A. Joseph and F. Mignot and F. Murat and B. Prum and
R. Rentschler",
booktitle = "Proceedings of the congress held at the Sorbonne and
Panth{\'e}on-Sorbonne Universities, Paris, July 6--10,
1992",
title = "First {European Congress} of {Mathematics}. {Vol}.
{III}",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xxx + 574",
year = "1994",
ISBN = "3-7643-2800-2; 3-7643-5156-X",
note = "Round tables.",
}
@Proceedings{Joseph:1994:FECa,
editor = "A. Joseph and F. Mignot and F. Murat and B. Prum and
R. Rentschler",
booktitle = "Proceedings of the congress held at the Sorbonne and
Panth{\'e}on-Sorbonne Universities, Paris, July 6--10,
1992",
title = "First {European Congress} of {Mathematics}. {Vol}.
{I}",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "lxii + 547",
year = "1994",
ISBN = "3-7643-2798-7",
note = "Invited lectures. Part 1.",
}
@Proceedings{Joseph:1994:FECb,
editor = "A. Joseph and F. Mignot and F. Murat and B. Prum and
R. Rentschler",
booktitle = "Proceedings of the congress held at the Sorbonne and
Panth{\'e}on-Sorbonne Universities, Paris, July 6--10,
1992",
title = "First {European Congress} of {Mathematics}. {Vol}.
{II}",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xxviii + 513",
year = "1994",
ISBN = "3-7643-2799-5",
note = "Invited lectures. Part 2.",
}
@Proceedings{Kohn:1989:RMC,
editor = "R. V. Kohn and G. W. Milton",
booktitle = "Proceedings of the SIAM Workshop held in Leesburg,
Virginia, December 7--10, 1988",
title = "Random media and composites (Leesburg, {VA}, 1988)",
publisher = "Society for Industrial and Applied Mathematics
(SIAM)",
address = "Philadelphia, PA",
pages = "viii + 214",
year = "1989",
ISBN = "0-89871-246-7",
}
@Proceedings{Markov:1999:PNI,
editor = "K. Markov and E. Inan",
title = "Proceedings of the Ninth International Symposium on
Continuum Models and Discrete Systems: 29 June--3 July
1998, Istanbul, Turkey",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xviii + 852",
year = "1999",
ISBN = "981-02-3669-7",
LCCN = "QA808.2.I586 1998",
}
@Proceedings{Maso:1991:CMH,
editor = "G. {Dal Maso} and G. Dell'Antonio",
booktitle = "Proceedings of the workshop held in Trieste, January
15--26, 1990",
title = "Composite media and homogenization theory",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xiv + 258",
year = "1991",
ISBN = "0-8176-3511-4",
}
@Proceedings{Olhoff:1995:PFW,
editor = "N. Olhoff and G. I. N. Rozvany",
booktitle = "Proceedings of the First World Congress of Structural
and Multidisciplinary Optimization: 28 May--2 June
1995, Goslar, Germany: WCSMO-1",
title = "Proceedings of the First World Congress of Structural
and Multidisciplinary Optimization: 28 May--2 June
1995, Goslar, Germany: {WCSMO}-1",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xxvii + 964",
year = "1995",
ISBN = "0-08-042267-5",
LCCN = "TA645 .W65 1995",
}
@Proceedings{Papanicolaou:1998:WPC,
editor = "G. Papanicolaou",
booktitle = "Proceedings of the IMA Workshops on Wavelets,
Multigrid and Other Fast Algorithms (Multiple, FFT) and
Their Use in Wave Propagation and Waves in Random and
Other Complex Media held at the University of
Minnesota, Minneapolis, MN, 1994",
title = "Wave propagation in complex media",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 287",
year = "1998",
ISBN = "0-387-98309-0",
LCCN = "QA927 .W378 1998",
MRnumber = "MR98g:00033",
}
@Proceedings{Pedersen:1993:ODA,
editor = "P. Pedersen",
booktitle = "Optimal Design with Advanced Materials: the Frithiof
Niordson volume: proceedings of the IUTAM Symposium on
Optimal Design with Advanced Materials, Lyngby,
Denmark, 18--20 August 1992",
title = "Optimal Design with Advanced Materials: the Frithiof
Niordson volume: proceedings of the {IUTAM} Symposium
on Optimal Design with Advanced Materials, Lyngby,
Denmark, 18--20 August 1992",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "xii + 515",
year = "1993",
ISBN = "0-444-89869-7",
LCCN = "TA658.8 .I98 1992",
}
@Proceedings{Soares:1987:CAO,
editor = "C. A. {Mota Soares}",
title = "Computer Aided Optimal Design: Structural and
Mechanical Systems",
volume = "27",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 1029",
year = "1987",
ISBN = "0-387-17598-9",
LCCN = "TA174 .N3651 1986",
series = "NATO ASI series. Series F, Computer and systems
sciences",
}