On the singular set of $\mathrm{BV}$ minimizers for non-autonomous functionals

Abstract

We investigate regularity properties of minimizers for non-autonomous convex variational integrands $F(x,\mathrm{D}u)$ with linear growth, defined on bounded Lipschitz domains $\Omega \subset {\mathbb{R}}^n$. Assuming appropriate ellipticity conditions and Hölder continuity of ${\mathrm{D}}_{z}F(x,z)$ with respect to the first variable, we establish higher integrability of the gradient of minimizers and provide bounds on the Hausdorff dimension of the singular set of minimizers.

Version 2, 26 pages, 1 figure. Final version to appear in Communications in Contemporary Mathematics

References in corpus (2)

• Regularity for double phase problems at nearly linear growth
• Regularity for multi-phase problems at nearly linear growth