On the convexity of some free boundaries
type: Item
instance of: scholarly article
title: On the convexity of some free boundaries
zbMATH Open document ID: 1180.35578
DOI: 10.4171/IFB/220
author: Antonio Greco
author: Bernd Kawohl
published in: Interfaces and Free Boundaries
publication date: 2010-02-02T00:00:00Z
full work available at URL: www.ems-ph.org
review text: Summary: We demonstrate that a method of Colesanti and Salani, which compares solutions of elliptic differential equations to their quasiconcave envelopes can be extended to derive convexity of free boundaries. As examples, we present the so-called dam problem, a free boundary problem modelling pollution and a Bernoulli problem. Moreover, we prove strict convexity of the wet region in the dam problem in arbitrary dimensions.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 5665699
zbMATH Keywords: quasiconcave envelopes
zbMATH Keywords: pollution
zbMATH Keywords: Bernoulli problem
zbMATH Keywords: dam problem
MaRDI profile type: Publication
OpenAlex ID: W1998013167
description: scientific article; zbMATH DE number 5665699