Sobolev regularity for Convex Functionals on BD

TL;DR

This paper investigates Sobolev regularity of minimizers for convex variational problems depending on the symmetric gradient, extending BV results to cases where full gradients are not Radon measures.

Contribution

It extends Sobolev regularity results from BV to convex functionals depending on symmetric gradients without assuming full gradient measures.

Findings

Established Sobolev regularity for minimizers in the symmetric gradient setting.

Extended regularity results to functionals with linear growth depending on symmetric gradients.

Bridged the gap between BV theory and symmetric gradient functionals.

Abstract

We study Sobolev regularity results for minimisers of autonomous, convex variational of linear growth which depend on the symmetric gradient rather than the full gradient. This extends the results available in the literature for the BV-setting to the case of functionals whose full gradients are a priori not known to exist as matrix-valued Radon measures.