Variational Principles Bounds, and Size Effects for Composites with Nonstandard Interfacial Transmission Conditions. by Robert Lipton, WPI AEB 350, 3:15pm Monday, April 22, 1996 Abstract New variational principles are given for multi-phase composites with nonstandard transmission conditions between phases. Extra geometric information is incoded into the principles through the solution operators of simpler transport problems. These operators can be expressed as gradients of simple layer potentials with densities supported on phase interfaces or in terms or simple Dirichlet problems inside each phase region. The resulting bounds predict new size effect phenomena. Request for preprints and reprints lipton@WPI.EDU This source can be found at http://www.math.utah.edu/research/