Korn-type inequalities in orlicz-sobolev spaces involving the trace-free part of the symmetric gradient and applications to regularity theory

Dominic Breit, Oliver D. Schirra

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2 Citations (Scopus)

Abstract

We prove variants of Korn's inequality involving the trace-free part of the symmetric gradient of vector fields v : Omega -> R-n (Omega subset of R-n), that is,

f(Omega)(h(vertical bar del nu vertical bar) (dx)

for functions with zero trace as well as some further variants of this inequality. Here, h is an N-function of rather general type. As an application we prove partial regularity of of minimizers of energies of the type f(Omega) h(vertical bar epsilon(D)(v)vertical bar) dx, occurring, for example, in general relativity.

Original languageEnglish
Pages (from-to)335-356
Number of pages22
JournalZeitschrift für Analysis und ihre Anwendungen
Volume31
Issue number3
DOIs
Publication statusPublished - 2012

Keywords

  • Generalized Korn inequalities in Orlicz-Sobolev spaces
  • variational problems
  • nonstandard growth
  • regularity
  • HIGHER INTEGRABILITY
  • GEOMETRIC RIGIDITY
  • OPERATORS
  • DOMAINS
  • GROWTH

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