Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 29, Issue -, Pages -Publisher
EDP SCIENCES S A
DOI: 10.1051/cocv/2023062
Keywords
Free-discontinuity problems; p(x)-growth; regularity; minimizers
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This study proves a regularity result for free-discontinuity energies defined on the space SBVp() of special functions of bounded variation with variable exponent, assuming a log-Holder continuity for the variable exponent p(x). The analysis expands on the regularity theory for minimizers of a class of free-discontinuity problems in the nonstandard growth case.
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-Holder 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.
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