Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case
type: Item
instance of: scholarly article
title: Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case
zbMATH Open document ID: 1096.35044
author: Jean Dolbeault
author: P. Felmer
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
full work available at URL: http://hdl.handle.net/10533/175041
review text: The authors consider solutions of the semilinear elliptic partial differential equation \[ \Delta u+f(u)=0,\quad x\in\Omega\subset\mathbb{R}^N \tag{1} \] which are nonnegative and vanishing at the boundary. The goal of the authors is to analyze the symmetry and the related monotonicity question for nonlinearities that are continuous but not Lipschitz continuous. The basic tools in the proof are a local variant of the moving plane method and the unique continuation principle.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 2102585
zbMATH Keywords: monotonicity and symmetry properties
zbMATH Keywords: non-Lipschitz case
zbMATH Keywords: positive solution
zbMATH Keywords: squalar field equation
zbMATH Keywords: moving plane
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2015565214
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DOI: 10.1016/J.NA.2004.04.007
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description: scientific article; zbMATH DE number 2102585