A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems
type: Item
instance of: scholarly article
title: A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems
zbMATH Open document ID: 0733.35024
DOI: 10.1007/BF00376141
author: Hi Jun Choe
published in: Archive for Rational Mechanics and Analysis
publication date: 1991-01-01T00:00:00Z
review text: Let \(u\in W^{1,p}(\Omega)\) be a solution of the variational inequality \[ \int_{\Omega}| Du|^{p-2} Du(Dv-Du)dx\geq \int_{\Omega}b(x,u,Du)(v-u)dx+\int_{\Omega}f(x)(Dv-Du)dx \] for all \(v\in \{W_ 0^{1,p}(\Omega)+u_ 0\}\), v(x)\(\geq \psi (x)\) a.e. in \(\Omega\), where \(u_ 0\in W^{1,p}(\Omega)\) and \(u_ 0(x)\geq \psi (x)\). Under appropriate conditions on b and f the author shows that \(u\in C_{loc}^{0,\alpha}(\Omega)\) when \(\psi =\in W_{loc}^{1,m}(\Omega)\) \((m>n)\) and \(u\in C_{loc}^{1,\alpha}(\Omega)\) when \(\psi \in W_{loc}^{1,\beta}(\Omega)\) \((\alpha >0)\) for some suitable \(\beta >0\).
reviewed by: Giovanni Porru
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 4212573
zbMATH Keywords: Hölder continuity
zbMATH Keywords: obstacle problems
zbMATH Keywords: variational inequality
MaRDI profile type: Publication
cites work: On the Obstacle Problem for Quasilinear Elliptic Equations of p Laplacian Type
cites work: C1 + α local regularity of weak solutions of degenerate elliptic equations
cites work: Hölder continuity of the gradient for degenerate variational inequalities
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: Q3216972
cites work: The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
cites work: Regularity for minima of functionals with p-growth
cites work: Interior regularity for solutions to obstacle problems
cites work: Q3781648
cites work: Local behavior of solutions of quasi-linear equations
cites work: On harnack type inequalities and their application to quasilinear elliptic equations
full work available at URL: https://doi.org/10.1007/bf00376141
OpenAlex ID: W1978908638
description: scientific article; zbMATH DE number 4212573