English

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

Analysis of PDEs 2023-05-08 v2

Abstract

A regularity result for free-discontinuity energies defined on the space SBVp()SBV^{p(\cdot)} of special functions of bounded variation with variable exponent is proved, under the assumption of a log-H\"older continuity for the variable exponent p(x)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

Cite

@article{arxiv.2303.01951,
  title  = {Regularity of minimizers for free-discontinuity problems with $p(\cdot)$-growth},
  author = {Chiara Leone and Giovanni Scilla and Francesco Solombrino and Anna Verde},
  journal= {arXiv preprint arXiv:2303.01951},
  year   = {2023}
}