Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
type: Item
instance of: scholarly article
title: Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
zbMATH Open document ID: 0853.35049
DOI: 10.2307/2118531
author: Luis Caffarelli
author: Sandro Salsa
author: I. Athanasopoulos
published in: Annals of Mathematics. Second Series
publication date: 1996-07-18T00:00:00Z
review text: This work examines \(\lambda\)-caloric functions which are nonnegative solutions of the heat equation \(\Delta u- \lambda u_t= 0\) \((\lambda> 0)\) in some domain that vanishes locally on some distinguished part of the boundary. Caloric functions in Lipschitz domains are shown to be monotone in any direction going into the domain. Regularity of solutions of certain free boundary problems across the transition surface is developed, which involves the study of asymptotic behavior of caloric functions on the boundary.
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 906871
zbMATH Keywords: phase transition problems
zbMATH Keywords: caloric functions
reviewed by: Suzanne Lenhart
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118531
OpenAlex ID: W2330384007
description: scientific article; zbMATH DE number 906871