Partial regularity of solutions of nonlinear quasimonotone systems
type: Item
instance of: scholarly article
title: Partial regularity of solutions of nonlinear quasimonotone systems
zbMATH Open document ID: 1125.35345
author: Christoph Hamburger
published in: Hokkaido Mathematical Journal
publication date: 2004-03-08T00:00:00Z
review text: Vector-valued weak solutions of the nonlinear system \(\text{div}\;A(x,u,Du)+B(x,u,Du)=0\) are studied, assuming strict quasimonotonicity on \(A\) and some natural polynomial growth, as well as Hölder continuity of \(A\) in the first and second and differentiability in the third variable. Moreover, it is assumed that \(A(x,u,P)\cdot P\geq F(x,P)\) for some continuous function \(F\) which is strictly quasiconvex at zero. Under such conditions, it is proved that weak solutions have Hölder continuous derivatives almost everywhere, with optimal Hölder exponent. The proof is an indirect blow-up argument, using higher integrability.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 2053122
zbMATH Keywords: partial regularity
zbMATH Keywords: weak solution
zbMATH Keywords: nonlinear system
zbMATH Keywords: quasilinear system
zbMATH Keywords: quasi-monotonicity
zbMATH Keywords: ellipticity
zbMATH Keywords: natural growth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350657525
OpenAlex ID: W1995946994
DOI: 10.14492/HOKMJ/1350657525
description: scientific article; zbMATH DE number 2053122