Multiphase double‐porosity homogenization for perimeter functionals
Margherita Solci · Mathematical Methods in the Applied Sciences · 2012
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 R n ∖ E is composed of disjoint compact components. Assuming E to be the union of a finite number N of connected components E 1 , … , 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. Copyright © 2012 John Wiley & Sons, Ltd.