Full regularity for a class of degenerated parabolic systems in two spatial variables
type: Item
instance of: scholarly article
title: Full regularity for a class of degenerated parabolic systems in two spatial variables
zbMATH Open document ID: 0931.35029
published in: Manuscripta Mathematica
publication date: 2000-02-23T00:00:00Z
review text: The authors consider a quasilinear parabolic system (1) \(\partial_t u-\text{div} a(\nabla u)=0\). It is supposed that \(u:Q\to\mathbb{R}^N\), where \(Q=\Omega\times]0,T[\), \(T\) is a fixed positive parameter, and \(\Omega\) is a bounded domain. The function \(a\) has \(p\)-growth behaviour, \(1<p<\infty\), and the ellipticity ``constant'' behaves like \((1+|\nabla u|)^{p-2}\). The authors prove full regularity of the weak solution in interior subdomains, but globally in time: any weak solution of the system (1) is Hölder continuous in \(Q\).
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1339451
zbMATH Keywords: Hölder continuity
author: Jens Frehse
author: G. Seregin
MaRDI profile type: Publication
full work available at URL: s002290050189
OpenAlex ID: W2012042039
DOI: 10.1007/S002290050189
description: scientific article; zbMATH DE number 1339451