Homogenization of a quasilinear elliptic problem in porous media with Robin-type conditions and L¹ data

Abstract

We consider a class of quasilinear elliptic problems with L¹ data, set in a domain periodically perforated by two kinds of holes. A Robin-type condition depending on a parameter γ is imposed on the boundary of some holes, while a Dirichlet condition is prescribed on the boundary of the remaining holes as well as on the external boundary of the domain. Our goal is to describe the asymptotic behavior of the renormalized solution of this problem, given that the solution does not belong to H¹ and to derive the corresponding limit problem.