Homogenization of elliptic problems with the Dirichlet and Neumann conditions imposed on varying subsets
Carmen Calvo‐Jurado, Juan Casado‐Díaz, Manuel Luna‐Laynez · Mathematical Methods in the Applied Sciences · 2007
Abstract We study the asymptotic behaviour of the solution un of a linear elliptic equation posed in a fixed domain Ω. The solution un is assumed to satisfy a Dirichlet boundary condition on Γn, where Γn is an arbitrary sequence of subsets of ∂Ω, and a Neumman boundary condition on the remainder of ∂Ω. 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. Copyright © 2007 John Wiley & Sons, Ltd.