Convexity estimates for nonlinear elliptic equations and application to free boundary problems
type: Item
instance of: scholarly article
title: Convexity estimates for nonlinear elliptic equations and application to free boundary problems
zbMATH Open document ID: 1034.35047
DOI: 10.1016/S0294-1449(02)00106-3
author: Jean Dolbeault
author: Régis Monneau
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2003-04-14T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78566
review text: The authors prove the convexity of the set which is delimited by the free boundary corresponding to a quasi-linear elliptic equation in a 2-dimensional convex domain. The method relies on the study of the curvature of the level lines at the points which realize the maximum of the normal derivative at a given level, for analytic solutions of fully nonlinear elliptic equations. The method also provides an estimate of the gradient in terms of the minimum of the curvature of the boundary of the domain, which is not necessarily assumed to be convex.
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1881302
zbMATH Keywords: quasi-linear elliptic equations
zbMATH Keywords: free boundary problem
zbMATH Keywords: gradient estimates
zbMATH Keywords: curvature of level sets
MaRDI profile type: Publication
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OpenAlex ID: W2037179361
description: scientific article; zbMATH DE number 1881302