The homogenization of elliptic partial differential systems on rugous domains with variable boundary conditions

This paper is devoted to studying the asymptotic behaviour of a sequence of elliptic systems posed in a sequence of rough domains Omega(n). The solutions u(n) are assumed to satisfy u(n)(x) is an element of V-n(x), where V-n(x) is a vectorial space depending on x is an element of (Omega) over bar (n). This enables one to consider several types of boundary conditions posed in variable sets of the boundary. For some choices of the vectorial spaces V-n(x), our study provides, in particular, some classical results for the homogenization of Dirichlet elliptic problems in varying domains.