% -*-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", }