Trace-Free Korn Inequalities in Orlicz Spaces

Dominic Breit, Andrea Cianchi, Lars Diening

Research output: Contribution to journalArticle

5 Citations (Scopus)
30 Downloads (Pure)

Abstract

Necessary and suffcient conditions are exhibited for a Korn-type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a byproduct of our approach, a positive answer is given to the question of the necessity of the same sufficient conditions in related Korn-type inequalities for the full symmetric gradient, for negative Orlicz-Sobolev norms, and for the gradient of the Bogovskii operator.

Original languageEnglish
Pages (from-to)2496-2526
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number4
DOIs
Publication statusPublished - 6 Jul 2017

Keywords

  • Korn inequality
  • Orlicz spaces
  • Singular integrals
  • Symmetric gradient
  • Trace-free symmetric gradient

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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