Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form
type: Item
instance of: scholarly article
title: Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form
zbMATH Open document ID: 0961.35035
DOI: 10.1023/A:1008670611142
author: Jana Björn
author: V. Maz'ya
published in: Potential Analysis
publication date: 2001-05-15T00:00:00Z
review text: The Dirichlet problem for the uniformly elliptic equation in divergence form \( \text{div} ( {\mathcal A}(x) \nabla u(x)) \) is considered in an open subset of \( \Omega \subset \mathbb{R}^{n} \). The coefficients of the equation are assumed to be bounded and measurable, whereas no assumption is made on the boundary of the open set \( \Omega \). A pointwise estimate of the solution is derived, improving previously existent estimates. As a particular case one can derive a new sufficient but not necessary condition for Hölder continuity at a boundary point of \( {\mathcal A} \)-harmonic functions vanishing on part of the boundary.
reviewed by: Antonio Bove
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 1436915
zbMATH Keywords: pointwise estimate
zbMATH Keywords: Hölder continuity
zbMATH Keywords: \({\mathcal A}\)-harmonic functions
MaRDI profile type: Publication
full work available at URL: a:1008670611142
OpenAlex ID: W1747837262
description: scientific article; zbMATH DE number 1436915