The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations
type: Item
instance of: scholarly article
title: The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations
zbMATH Open document ID: 1011.35055
DOI: 10.1007/BF02788085
author: Patrizia Pucci
author: James Serrin
published in: Journal d'Analyse Mathématique
publication date: 2002-07-10T00:00:00Z
review text: The authors consider the model quasilinear elliptic differential equation \[ \text{div} \biggl\{A\bigl( |Du|\bigr) Du\biggr\}-f(u)=0,\;u> 0 \tag{1} \] in \(\mathbb{R}^2\) and more generally, the two-sided differential inequality \[ -B(Du)\leq \text{div} \biggl\{A\bigl(|Du|\bigr) Du \biggr\} \leq B(Du)+f(u),\;u>0. \tag{2} \] Here, the authors use a maximum principle to obtain a Harnack inequality for (2).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1765850
zbMATH Keywords: maximum principle
zbMATH Keywords: two-sided differential inequality
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02788085
OpenAlex ID: W2009077111
description: scientific article; zbMATH DE number 1765850