Homogenization of the Poisson equation with Dirichlet conditions in random perforated domains

We consider a sequence of open sets O-epsilon contained in a fixed bounded open set O of R-N, N >= 3, which vary randomly with epsilon > 0. The corresponding distribution function is given by an ergodic measure preserving dynamical system in such a way that O\O-epsilon, is a union of closed sets of size epsilon(N/N-2) and the distance between them of order epsilon. For this sequence O-epsilon we study the asymptotic behavior of the solutions of the Poisson equation with Dirichlet conditions on partial derivative O-epsilon. Similarly to the classical Cioranescu-Murat result for the deterministic problem we show the existence of a new term of zero order in the limit equation. We emphasize the fact that this new term is deterministic. (C) 2014 Elsevier B.V. All rights reserved.