Boundedness and continuity of solutions to linear elliptic boundary value problems in two dimensions
type: Item
instance of: scholarly article
title: Boundedness and continuity of solutions to linear elliptic boundary value problems in two dimensions
zbMATH Open document ID: 0790.35025
DOI: 10.1007/BF01459758
author: Konrad Gröger
published in: Mathematische Annalen
publication date: 1994-06-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165193
review text: The paper deals with mixed boundary value problems for linear second order elliptic differential equations in a bounded two-dimensional Lipschitzian domain \(\Omega\). It is shown that the solutions to such problems are bounded and continuous provided that the right hand side \(g\) of the equation is such that \(g\log(1+ | g|)\in L^ 1(\Omega)\) and that the right hand side of the natural boundary condition has a similar property. The proof is based on results on the solvability of boundary value problems in the context of Sobolev spaces and on the introduction of some new interpolation spaces.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 46B70
zbMATH DE Number: 562484
zbMATH Keywords: boundedness
zbMATH Keywords: continuity
zbMATH Keywords: mixed boundary value problems
zbMATH Keywords: linear second order elliptic differential equations
zbMATH Keywords: bounded two-dimensional Lipschitzian domain
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: new interpolation spaces
MaRDI profile type: Publication
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OpenAlex ID: W365669208
description: scientific article; zbMATH DE number 562484