Korn-Type Inequalities in Orlicz-Sobolev Spaces Involving the Trace-Free Part of the Symmetric Gradient and Applications to Regularity Theory

  • Dominic Breit

    Universität des Saarlandes, Saarbrücken, Germany
  • Oliver D. Schirra

    Universität des Saarlandes, Saarbrücken, Germany

Abstract

We prove variants of Korn's inequality involving the trace-free part of the symmetric gradient of vector fields (), that is,

for functions with zero trace as well as some further variants of this inequality. Here, is an -function of rather general type. As an application we prove partial -regularity of minimizers of energies of the type occurring, for example, in general relativity.

Cite this article

Dominic Breit, Oliver D. Schirra, Korn-Type Inequalities in Orlicz-Sobolev Spaces Involving the Trace-Free Part of the Symmetric Gradient and Applications to Regularity Theory. Z. Anal. Anwend. 31 (2012), no. 3, pp. 335–356

DOI 10.4171/ZAA/1463