Published Paper

Inserted: 6 jul 2023
Last Updated: 28 aug 2024

Journal: Nonlinear Analysis
Volume: 247
Number: October 2024
Year: 2023
Doi: https://doi.org/10.1016/j.na.2024.113597

Abstract:

We study the regularity of local minimisers of a prototypical free-discontinuity problem involving both a manifold-valued constraint on the maps (which are defined on a bounded domain $\Omega \subset \mathbb{R}^2$) and a variable-exponent growth in the energy functional. To this purpose, we first extend to this setting the Sobolev approximation result for special function of bounded variation with small jump set originally proved by Conti, Focardi, and Iurlano \cite{CFI-ARMA, CFI-AIHP} for special functions of bounded deformation. Secondly, we use this extension to prove regularity of local minimisers.

Keywords: Sobolev approximation, manifold constrained