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

Let Ω be a sufficiently regular bounded connected open subset of Rn such that 0 ∈ Ω and that Rn∖clΩ is connected. Then we take q11, … ,qnn ∈ ]0,+ ∞ [and . If ε is a small positive number, then we define the periodically perforated domain , where {e1, … ,en} is the canonical basis of Rn. For ε small...

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Vydané v:	Mathematical methods in the applied sciences Ročník 35; číslo 3; s. 334 - 349
Hlavný autor:	Musolino, Paolo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Chichester, UK John Wiley & Sons, Ltd 01.02.2012
Predmet:	Boundary value problems for second-order elliptic equations integral equations methods integral operators integral representations integral representations, integral operators, integral equations methods Laplace operator periodically perforated domain real analytic continuation in Banach space singularly perturbed domain
ISSN:	0170-4214, 1099-1476
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Shrnutí:	Let Ω be a sufficiently regular bounded connected open subset of Rn such that 0 ∈ Ω and that Rn∖clΩ is connected. Then we take q11, … ,qnn ∈ ]0,+ ∞ [and . If ε is a small positive number, then we define the periodically perforated domain , where {e1, … ,en} is the canonical basis of Rn. For ε small and positive, we introduce a particular Dirichlet problem for the Laplace operator in the set . Namely, we consider a Dirichlet condition on the boundary of the set p + εΩ, together with a periodicity condition. Then we show real analytic continuation properties of the solution and of the corresponding energy integral as functionals of the pair of ε and of the Dirichlet datum on p + ε∂Ω, around a degenerate pair with ε = 0. Copyright © 2011 John Wiley & Sons, Ltd.
Bibliografia:	istex:6A06CD55F8A32D407C5F2AB159C603FCFDE64E22 ark:/67375/WNG-K6R1RPVJ-R ArticleID:MMA1575
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.1575