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 sever...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2013-04, Vol.143 (2), p.303-335
Main Authors: Casado-Díaz, J., Luna-Laynez, M., Suárez-Grau, F. J.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Boundary conditions
Dirichlet problem
Homogenization
Homogenizing
Partial differential equations
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210510001885