Multi-phase double-porosity homogenization for perimeter functionals

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 RnnE is composed of disjoint com- pact components. Assuming E to be the union of a finite number N of connected components E1, : : : , EN, the -limit F is a multiphase energy with a ’decoupled’ surface part, obtained by homogenization from the surface tensions in each Ej, a trivial bulk term obtained as a weak limit, and a further interacting term between the phases, involving an asymptotic for- mula for a family minimum problems on invading an asymptotic formula for a family of minimum problems on invading domains with prescribed boundary conditions.