Calculus of Variations and Geometric Measure Theory

C. Leone - G. Scilla - F. Solombrino - A. Verde

Regularity of minimizers for free-discontinuity problems with $p(\cdot)$-growth

created by scilla on 03 Mar 2023
modified by solombrino on 08 Nov 2023


Published Paper

Inserted: 3 mar 2023
Last Updated: 8 nov 2023

Journal: ESAIM: Control, Optimisation and Calculus of Variations
Volume: 29
Pages: 78
Year: 2023

ArXiv: 2303.01951 PDF


A regularity result for free-discontinuity energies defined on the space $SBV^{p(\cdot)}$ of special functions of bounded variation with variable exponent is proved, under the assumption of a log-Hölder continuity for the variable exponent $p(x)$. Our analysis expand on the regularity theory for minimizers of a class of free-discontinuity problems in the nonstandard growth case. This may be seen as a follow-up of the paper Fusco, Mingione and Trombetti (2001), dealing with a constant exponent.

Keywords: Free-discontinuity problems, regularity, Minimizers, $p(x)$-growth