Symmetry for degenerate parabolic equations
type: Item
instance of: scholarly article
title: Symmetry for degenerate parabolic equations
zbMATH Open document ID: 0697.35074
DOI: 10.1007/BF01053461
author: Giovanni Alessandrini
author: Nicola Garofalo
published in: Archive for Rational Mechanics and Analysis
publication date: 1989-01-01T00:00:00Z
review text: For \(0<T\leq \infty\), and \(\Omega \subset R^ n\) with boundary in \(C^ 2\), let \(C_ T\) be the cylinder \(\Omega\) \(\times (0,T)\). The authors study the equation \[ u_ t-div[a(u,| \nabla u|)\nabla u]=c(u,| \nabla u|) \] in \(C_ T\), a, and c are real valued functions satisfying suitable conditions of smoothness. They prove that under certain stated conditions \(\Omega\) is a ball and for every \(t\in (0,T)\) u(,t) is a non-decreasing radically symmetric function with respect to the center of the ball.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B99
zbMATH DE Number: 4142588
zbMATH Keywords: ball
zbMATH Keywords: radically symmetric
reviewed by: Hussain S. Nur
MaRDI profile type: Publication
cites work: Gradient estimates for degenerate diffusion equations II
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cites work: Q3782002
description: scientific article; zbMATH DE number 4142588