Some new monotonicity theorems with applications to free boundary problems.
type: Item
instance of: scholarly article
title: Some new monotonicity theorems with applications to free boundary problems.
zbMATH Open document ID: 1142.35382
DOI: 10.2307/3062121
published in: Annals of Mathematics. Second Series
publication date: 2002-11-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.annm/1032210018
review text: This paper is devoted to some new monotonicity theorems with applications to free boundary problems. More precisely, the authors reformulate the theorem so that it applies to inhomogeneous equations in which the right-hand side of the equation need not vanish at the free boundary. Here particular interest is the case in which \(\Delta u\) takes two different constant values on the set where \(u> 0\) and on the set where \(u< 0\). The new versions of the monotonicity theorem presented in the paper lead to existence of certain classical solutions to the Prandtl-Batchelor equation in two dimensions and partial regularity results in higher dimensions.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1779738
zbMATH Keywords: free boundary problems
zbMATH Keywords: Prandtl-Batchelor equation
zbMATH Keywords: monotonicity theorem
author: Luis Caffarelli
author: David Jerison
author: C. E. Kenig
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W1511208511
description: scientific article; zbMATH DE number 1779738