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Analysis

International mathematical journal of analysis and its applications

Editor-in-Chief: Schulz, Friedmar

4 Issues per year


CiteScore 2017: 0.66

SCImago Journal Rank (SJR) 2017: 0.564
Source Normalized Impact per Paper (SNIP) 2017: 0.674

Mathematical Citation Quotient (MCQ) 2017: 0.38

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2196-6753
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Volume 28, Issue 1

Issues

Asymptotic behavior of the solutions of the Dirichlet problem for the Laplace operator in a domain with a small hole. A functional analytic approach

Massimo Lanza de Cristoforis
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/anly.2008.0903

We consider a hypersurface in Rn parametrized by a diffeomorphism Φo of the unit sphere in Rn into Rn, and we take a point w in the domain I[Φo] enclosed by the image of Φo, and we consider the ‘hole’ R[w + εξ] enclosed by the image of the hypersurface w + εξ, where ξ is a diffeomorism as Φo with 0 ∈ I[ξ] and ε is a small positive real parameter. Then we consider the Dirichlet problem for the Laplace equation in the perforated domain I[Φo] with the hole I[w + εξ] removed and show real analytic continuation properties of the solution u and of the corresponding energy integral as functionals of the sextuple of w, ε, ξ, Φo, and of the Dirichlet data in the interior and exterior boundaries of the perforated domain, which we think of as a point in an appropriate Banach space, around a degenerate sextuple with ε = 0.

Keywords: Dirichlet boundary value problem; singularly perturbed domain; Laplace operator; real analytic continuation in Banach space

About the article

Received: 2006-04-07

Published Online: 2009-09-25

Published in Print: 2008-01-01


Citation Information: Analysis, Volume 28, Issue 1, Pages 63–93, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2008.0903.

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