Partial Regularity for Symmetric-Convex Functionals of Linear Growth

TL;DR

This paper proves partial regularity of minimizers for a class of variational problems involving symmetric gradients and linear growth, overcoming challenges posed by the lack of Korn inequality in the L^1 setting.

Contribution

It establishes partial regularity results for symmetric-convex functionals of linear growth without relying on Korn inequality, extending previous BV-based results.

Findings

Proves partial regularity of BD-minima under weak ellipticity.

Shows regularity results hold despite absence of Korn inequality in L^1.

Extends regularity theory to symmetric-gradient-based functionals.

Abstract

We establish partial regularity of BD-minima for variational integrals of linear growth which depend on the symmetric gradients and satisfy a weak ellipticity condition. Since there is no Korn Inequality in the $L^{1}$-Setup, the result does not follow from the respective result on BV due to Anzellotti and Giaquinta.