Higher integrability of the gradient in linear elasticity
type: Item
instance of: scholarly article
title: Higher integrability of the gradient in linear elasticity
zbMATH Open document ID: 0806.73009
DOI: 10.1007/BF01459793
author: Peter Shi
author: Steve Wright
published in: Mathematische Annalen
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165217
review text: The authors investigate higher integrability of the gradient of the solution to a displacement-traction problem that is defined on a bounded \(C^ 1\) domain of \(R^ n\) associated with the linear elasticity equations with \(L^ \infty\) coefficients. This result is established by use of the technique of reverse Hölder inequalities, in which certain interior and boundary estimates are obtained for a local Hardy-Littlewood maximal operator of the gradient. An appropriate interplay between the Sobolev-Poincaré inequality, the Korn inequality and the local geometry of the domain near the interface of the two different boundary conditions plays a major role in establishing these estimates.
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 683108
zbMATH Keywords: displacement-traction problem
zbMATH Keywords: reverse Hölder inequalities
zbMATH Keywords: local Hardy-Littlewood maximal operator
zbMATH Keywords: Sobolev-Poincaré inequality
zbMATH Keywords: Korn inequality
zbMATH Keywords: local geometry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 683108