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Homogenization of elliptic problems with the Dirichlet and Neumann conditions imposed on varying subsets
Author(s) -
CalvoJurado Carmen,
CasadoDíaz Juan,
LunaLaynez Manuel
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.857
Subject(s) - mathematics , homogenization (climate) , remainder , boundary value problem , dirichlet boundary condition , neumann boundary condition , mathematical analysis , dirichlet distribution , mixed boundary condition , elliptic boundary value problem , dirichlet problem , limit of a function , limit (mathematics) , arithmetic , biodiversity , ecology , biology
We study the asymptotic behaviour of the solution u n of a linear elliptic equation posed in a fixed domain Ω. The solution u n is assumed to satisfy a Dirichlet boundary condition on Γ n , where Γ n 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.