Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Free discontinuity problems
  • Gamma-convergence
  • integral representation
  • blow-up method

Mathematics Subject Classification

49J45, 49Q20, 74Q05, 74E30

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Suggested citation

G. Dal Maso, R. Toader. “Γ-Convergence and Integral Representation for a Class of Free Discontinuity Functionals.” Journal of Convex Analysis 31 (2024), No. 2, 411–476. https://doi.org/10.68381/jca31025

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.