Abstract

In this paper, we study a homogenization problem for perimeter energies in highly contrasted media; the analysis of the previous paper is carried out by removing the hypothesis that the perforated medium Rⁿ\E is composed of disjoint compact components. Assuming E to be the union of a finite number N of connected components E1, ..., E^N, the Γ-limit F is a multiphase energy with a ’decoupled’ surface part, obtained by homogenization from the surface tensions in each E^j, a trivial bulk term obtained as a weak limit, and a further interacting term between the phases, involving an asymptotic formula for a family minimum problems on invading an asymptotic formula for a family of minimum problems on invading domains with prescribed boundary conditions.

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