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HOMOGENIZATION OF ELLIPTIC PROBLEMS IN PERFORATED DOMAINS WITH MIXED BOUNDARY CONDITIONS

We consider a class of second order elliptic problems on perforated domains with small holes of size εδ, distributed periodically with the period ε. A non homogeneous Neumann condition is prescribed on the boundary of some holes; on the boundary of the other ones, it is a homogeneous Dirichlet condition that is considered. We are interested here to give the limit behaviour of the problems when ε→ 0 and δ = δ(ε)→ 0. To do so, we apply the periodic unfolding method introduced in [5], that allows us to consider general operators with highly oscillating (with ε) coe cients and rather general geometries.