Maximum principles for generalized solutions of quasi-linear elliptic equations
type: Item
instance of: scholarly article
title: Maximum principles for generalized solutions of quasi-linear elliptic equations
zbMATH Open document ID: 1141.35379
DOI: 10.1007/BF02439626
author: Xiaozeng Xu
author: Xiting Liang
author: Xiangdong Wang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2004-11-25T00:00:00Z
review text: This article considers quasi-linear equation \[ -\text{ div}A(x,u,\nabla u) +B(x,u,\nabla u)=0 \quad \text{ in }\;G, \] where \(G\) is a bounded domain in \(\mathbb R^{n}\), \(A(x,u,\xi)\) and \(B(x,u,\xi)\) are ``Carathéodory'' functions, satisfying certain elliptic and growth conditions. The authors prove that if a bounded generalized solution \(u\) is not a constant, then \[ \text{ ess\;sup}_{G'}u< \text{ ess\;sup}_{G}u, \quad\forall\;G'\subset\subset G. \]
reviewed by: Ning Su
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 2118933
zbMATH Keywords: quasi-linear elliptic equation
zbMATH Keywords: generalized solution
zbMATH Keywords: maximum principle
MaRDI profile type: Publication
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cites work: Q4205792
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full work available at URL: https://doi.org/10.1007/bf02439626
OpenAlex ID: W2077989533
description: scientific article; zbMATH DE number 2118933