Abstract
A regularity result for free-discontinuity energies defined on the spaceSBVp(·)of special functions of bounded variation with variable exponent is proved, under the assumption of a log-Hölder continuity for the variable exponentp(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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