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Journal of Convex Analysis 31 (2024), No. 2, 411--476
Copyright Heldermann Verlag 2024

Γ-Convergence and Integral Representation for a Class of Free Discontinuity Functionals

Gianni Dal Maso
SISSA, Trieste, Italy

Rodica Toader
(1) Dept. of Mathematics, Informatics and Geosciences, University of Trieste, Trieste, Italy
(2) D.M.I.F., UniversitÓ di Udine, Udine, Italy

We study the Γ-limits of sequences of free discontinuity functionals with linear growth, assuming that the surface energy density is bounded. We determine the relevant properties of the Γ-limit, which lead to an integral representation result by means of integrands obtained by solving some auxiliary minimum problems on small cubes.

Keywords: Free discontinuity problems, Gamma-convergence, integral representation, blow-up method.

MSC: 49J45, 49Q20, 74Q05, 74E30.

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