Strong Existence for Free-Discontinuity Problems with Nonstandard Growth
Copyright policy )Strong Existence for Free-Discontinuity Problems with Nonstandard Growth
An Ahlfors-type regularity result for free-discontinuity energies defined on the space $SBV^φ$ of special functions of bounded variation with $φ$-growth, where $φ$ 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.
arXiv admin note: text overlap with arXiv:2303.01951
nonstandard growth, regularity, Methods involving semicontinuity and convergence; relaxation, Smoothness and regularity of solutions to PDEs, free-discontinuity energy, minimizers, Ahlfors-type regularity, free-discontinuity problems, nonstandard growth, regularity, minimizers, quasi-minimizer, free-discontinuity problems; minimizers; nonstandard growth; regularity, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), 49J45, 46E30, 35B65, Mathematics - Analysis of PDEs, free-discontinuity problems, FOS: Mathematics, Analysis of PDEs (math.AP)
nonstandard growth, regularity, Methods involving semicontinuity and convergence; relaxation, Smoothness and regularity of solutions to PDEs, free-discontinuity energy, minimizers, Ahlfors-type regularity, free-discontinuity problems, nonstandard growth, regularity, minimizers, quasi-minimizer, free-discontinuity problems; minimizers; nonstandard growth; regularity, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), 49J45, 46E30, 35B65, Mathematics - Analysis of PDEs, free-discontinuity problems, FOS: Mathematics, Analysis of PDEs (math.AP)
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