A functional analytic approach for a singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain

Paolo Musolino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)

Abstract

We consider a sufficiently regular bounded open connected subset Ω of Rn such that 0εΩ and such that Rn/clΩ is connected. Then we choose a point wε]0, 1 [n. If e is a small positive real number, then we define the periodically perforated domain T(ε)≡Rn/∪ zεZncl(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.

Original languageEnglish
Pages (from-to)928-931
Number of pages4
JournalAIP Conference Proceedings
Volume1281
DOIs
Publication statusPublished - Sept 2010

Keywords

  • Dirichlet boundary value problem
  • Laplace operator
  • periodically perforated domain
  • real analytic continuation in Banach space
  • singularly perturbed domain

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