Locally uniform approximation by solutions of the classical Dirichlet problem
type: Item
instance of: scholarly article
title: Locally uniform approximation by solutions of the classical Dirichlet problem
zbMATH Open document ID: 0773.31010
DOI: 10.1007/BF01047673
author: Wolfhard Hansen
author: Ivan Netuka
published in: Potential Analysis
publication date: 1993-06-29T00:00:00Z
review text: Let \(U\) be an open subset of a \({\mathcal P}\)-harmonic space. It is shown that, in the topology of local uniform convergence, the space of classical solutions of the Dirichlet problem on \(U\) is dense in the space of Perron-Wiener-Brelot solutions of the Dirichlet problem if and only if the irregular boundary points of \(U\) form a set of harmonic measure 0.
Mathematics Subject Classification ID: 31D05
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 220430
zbMATH Keywords: harmonic space
zbMATH Keywords: irregular boundary points
reviewed by: D. H. Armitage
MaRDI profile type: Publication
cites work: Potential theory. An analytic and probabilistic approach to balayage
cites work: Q5793995
cites work: Sur un théorème de prolongement fonctionnel de Keldych concernant le problème de Dirichlet
cites work: Q5662251
cites work: Q5666837
cites work: Q4028745
description: scientific article; zbMATH DE number 220430