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

Paolo Musolino*

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

2 Dyfyniadau(SciVal)

Crynodeb

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.

Iaith wreiddiolSaesneg
Tudalennau (o-i)928-931
Nifer y tudalennau4
CyfnodolynAIP Conference Proceedings
Cyfrol1281
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - Medi 2010

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