The homogenization of elliptic partial differential systems on rugous domains with variable boundary conditions
Juan Casado‐Díaz, Manuel Luna‐Laynez, Francisco J. Suárez‐Grau · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2013
This paper is devoted to studying the asymptotic behaviour of a sequence of elliptic systems posed in a sequence of rough domains Ω n . The solutions u n are assumed to satisfy u n ( x ) ϵ V n ( x ), where V n ( 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 V n ( x ), our study provides, in particular, some classical results for the homogenization of Dirichlet elliptic problems in varying domains.