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A Functional Analytic Approach for a Singularly Perturbed Dirichlet Problem for the Laplace Operator in a Periodically Perforated Domain.
- Source :
- AIP Conference Proceedings; 9/30/2010, Vol. 1281 Issue 1, p928-931, 4p
- Publication Year :
- 2010
-
Abstract
- We consider a sufficiently regular bounded open connected subset Ω of R<superscript>n</superscript> such that 0εΩ and such that R<superscript>n</superscript>/clΩ is connected. Then we choose a point wε]0, 1 [<superscript>n</superscript>. If e is a small positive real number, then we define the periodically perforated domain T(ε)≡R<superscript>n</superscript>/∪<subscript>zεZ<superscript>n</superscript></subscript>cl(w+εΩ+z). For each small positive ε, we introduce a particular Dirichlet problem for the Laplace operator in the set T(ε). More precisely, we consider a Dirichlet condition on the boundary of the set w+εΩ, and we denote the unique periodic solution of this problem by u[ε]. Then we show that (suitable restrictions of) u[ε] can be continued real analytically in the parameter ε around ε = 0. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 1281
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 53768756
- Full Text :
- https://doi.org/10.1063/1.3498645