Boundary layer techniques for deriving the effective properties of composite materials

In this paper we present mathematically rigorous derivations of asymptotic expansions of the effective electrical conductivity of periodic dilute composites in terms of the volume fraction occupied by the inclusions. Our derivations are based on layer potential techniques, and valid for high contrast mixtures and inclusions with Lipschitz boundaries. They are motivated by the practically important inverse problem of determining the volume fraction of a suspension of complicated shaped particles from boundary measurements of voltage potentials.