Nearly Singular Fields: Electrostatics and Elastostatics of Composite Materials

Abstract

Abstract A classical problem in materials science involves the determination of effective transport properties in composites. The simplest problem is perhaps described by the second order elliptic partial differential equation where σ is piecewise constant, supplemented by suitable boundary conditions or by a radiation condition at infinity. This is a standard model for steady-state heat conduction and conductivity. For our purposes, it will be more convenient to rewrite (1) as an interface problem; we seek a potential function u which is harmonic in each component, continuous, and satisfies the continuity of flux condition