Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
type: Item
instance of: scholarly article
title: Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
zbMATH Open document ID: 0878.35029
DOI: 10.1016/S0021-7824(97)89945-X
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1997-06-23T00:00:00Z
review text: The authors present a solution to Dirichlet and Neumann boundary value problems for the Laplace equation on an exterior domain in \(\mathbb{R}^n\). Instead of imposing explicit asymptotic conditions at infinity they require that the solution be from an appropriate weighted Sobolev space with power-logarithmic weights. This appears advantageous for both the theoretical and numerical approach because it enables to control not only the behaviour of the gradient but also of the solution itself. The boundary of the domain is considered to be Lipschitz-continuous if \(p=2\) and of the class \(\mathcal C^{1,1}\) if \(p\neq2\).
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1010947
zbMATH Keywords: exterior domain
zbMATH Keywords: weighted Sobolev space
author: Chérif Amrouche
author: V. Girault
author: Jean Giroire
reviewed by: Jiří Rákosník
MaRDI profile type: Publication
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Wikidata QID: Q126351502
full work available at URL: s0021-7824(97)89945-x
OpenAlex ID: W2039052667
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description: scientific article; zbMATH DE number 1010947