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. 335–356DOI 10.4171/ZAA/1463