Calculus of Variations and Homogenization

Abstract

In this paper we study a class of problems which includes the following example. Let Ω be an open subset of ℝ^N and let ω be a measurable subset of Ω with given measure ϒ’. Let a(x) = α on ω and β on Ω\ω, and define u by div (a grad u) = 1 in Ω and u = 0 on the boundary. We want to find an ω which maximizes f^Ωu(x)dx among all the measurable sets ω with given measure ϒ’.