Optimal design with small contrast

Abstract

This paper is concerned with optimal design problems where we assume that the coefficients in the state equation have small contrast. Making an asymptotic expansion up to second order with respect to the contrast greatly simplifies the optimization problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that optimal microstructures are always simple laminates.