Hölder continuity of the gradient of the solutions of certain degenerate parabolic equations
type: Item
instance of: scholarly article
title: Hölder continuity of the gradient of the solutions of certain degenerate parabolic equations
zbMATH Open document ID: 0663.35040
author: Yazhe Chin
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: This paper is concerned with the parabolic equation \[ \partial u/\partial t-div(| \nabla u|^{p-2}\nabla u)=0,\quad x\in \Omega \subset {\mathbb{R}}^ N,\quad t>0 \] with \(p>\max \{3/2,2N/(N+2)\}\) which is degenerate if \(p<2\) or singular if \(3/2<p<2\). Let u(x,t) be any weak solution of the equation in \(L^{\infty}[0,T;L^ 2(\Omega)]\cap L^ p[0,T;W^{1,p}(\Omega)].\) The Hölder continuity of \(\nabla u\) is established.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 4084169
zbMATH Keywords: degenerate parabolic equations
zbMATH Keywords: weak solution
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4084169