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 Ωn. The solutions un are assumed to satisfy un(x) ϵ Vn(x), where Vn(x) is a vectorial space depending on $\smash{x\in\bar\varOmega_n}$. This enables one to consider several types of boundary conditions posed in variable sets of the boundary. For some choices of the vectorial spaces Vn(x), our study provides, in particular, some classical results for the homogenization of Dirichlet elliptic problems in varying domains.