Homogenization of elliptic problems with the Dirichlet and Neumann conditions imposed on varying subsets

We study the asymptotic behaviour of the solution un of a linear elliptic equation posed in a fixed domain (omega). The solution un is assumed to satisfy a Dirichlet boundary condition on (gamma)n, where (gamma)n is an arbitrary sequence of subsets of (partial)(omega), and a Neumman boundary condition on the remainder of (partial)(omega). We obtain a representation of the limit problem which is stable by homogenization and where it appears a generalized Fourier boundary condition. We also prove a corrector result.