
Journal of Convex Analysis 31 (2024), No. 2, 411476 Copyright Heldermann Verlag 2024 ΓConvergence 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., Università di Udine, Udine, Italy rodica.toader@units.it We study the Γlimits of sequences of free discontinuity functionals with linear growth, assuming that the surface energy density is bounded. We determine the relevant properties of the Γlimit, 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, Gammaconvergence, integral representation, blowup method. MSC: 49J45, 49Q20, 74Q05, 74E30. [ Fulltextpdf (385 KB)] for subscribers only. 