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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
dalmaso@sissa.it

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



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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