Strong existence for free-discontinuity problems with non-standard growth

An Ahlfors-type regularity result for free-discontinuity energies defined on the space $SB{V}^{\phi }$ of special functions of bounded variation with $\phi$-growth, where $\phi$ is a generalized Orlicz function, is proved. Our analysis expands on the regularity theory for minimizers of a class of free-discontinuity problems in the non-standard growth case.