Removability of singularities in potential theory
type: Item
instance of: scholarly article
title: Removability of singularities in potential theory
zbMATH Open document ID: 0795.31007
DOI: 10.1007/BF01047839
author: V. Pereyra
published in: Potential Analysis
publication date: 1994-06-07T00:00:00Z
review text: Etant donné un ouvert \(G\) de \(\mathbb{R}^ N\), un opérateur différentiel linéaire \(P(D)\) à coefficients \(\in{\mathcal C}^ \infty(G)\) et une partie fermée \(F\) de \(G\), on établit des conditions, les unes suffisantes, les autres nécessaires, pour que toute \(u\in{\mathcal L}^ 1_{\text{loc}}(G)\) solution (au sens des distributions) de \(P(D)u= 0\) sur \(G\backslash F\) soit aussi solution de la même équation sur \(G\). Les premières sont des estimations, pour \(x\in G\backslash F\) tendant vers \(F\), de \(u(x)\) en fonction de la distance de \(x\) à \(F\) dans une métrique anisotrope associée à l'opérateur \(P(D)\); les secondes, particulières au cas où les coefficients de \(P(D)\) sont constants, portent sur une mesure de Hausdorff relative à la même métrique.
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 554335
zbMATH Keywords: necessary and sufficient conditions
reviewed by: Rose-Marie Hervé
MaRDI profile type: Publication
cites work: Q5583306
cites work: Removable singularities of the functional wave equation
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full work available at URL: https://doi.org/10.1007/bf01047839
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description: scientific article; zbMATH DE number 554335