| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 78 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2023062 | |
| Published online | 08 November 2023 | |
Regularity of minimizers for free-discontinuity problems with p(·)-growth
Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126 Naples, Italy
* Corresponding author: chileone@unina.it
Received:
7
March
2023
Accepted:
18
August
2023
A regularity result for free-discontinuity energies defined on the space SBVp(·) 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 expands 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 N. Fusco et al., J. Convex Anal. 8 (2001) 349-367, dealing with a constant exponent.
Mathematics Subject Classification: 49J45 / 46E30 / 35B65
Key words: Free-discontinuity problems / p(x)-growth / regularity / minimizers
© The authors. Published by EDP Sciences, SMAI 2023
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