Local \({W^{2,m(\cdot)}_{loc}}\) regularity for \(p\)(.)-Laplace equations
type: Item
instance of: scholarly article
title: Local \({W^{2,m(\cdot)}_{loc}}\) regularity for \(p\)(.)-Laplace equations
zbMATH Open document ID: 1266.35061
author: Yanyan Li
published in: Manuscripta Mathematica
publication date: 2013-03-18T00:00:00Z
review text: The paper under review deals with the study of the local regularity of the weak solutions to a class of nonlinear elliptic equations with a variable exponent. Since in general solutions are not of class \(C^2_{loc}\), it is an important issue to study the summability of the second derivatives of the solutions. The main idea in the proof is to linearize the equation and then to exploit it by means of good appropriate test functions. Then there are established some uniform estimates on the second derivatives, which enable the authors to deduce the regularity properties by passing to the limiting problem.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6145954
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: regularity of solution
MaRDI profile type: Publication
full work available at URL: s00229-012-0549-y
OpenAlex ID: W2012268420
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DOI: 10.1007/S00229-012-0549-Y
description: scientific article; zbMATH DE number 6145954