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arXiv · 2303.01951

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

Chiara Leone·Giovanni Scilla·Francesco Solombrino·Anna Verde
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Abstract

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-H\"older 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.

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Chiara Leone, Giovanni Scilla, Francesco Solombrino, Anna Verde. 2023-03-03. Regularity of minimizers for free-discontinuity problems with $p(\cdot)$-growth. https://arxiv.org/abs/2303.01951

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