Inserted: 23 jun 2004
Last Updated: 20 dec 2006
Journal: Calc. Var. Partial Differential Equations.
We consider a class of functionals which are defined in the spaces $SBV$ and $SBD$ and do not depend on the traces $u^\pm$ on the set of discontinuity. In this work we prove that it is possible to approximate this energies, in the sense of $\Gamma$-convergence, by means of a family of non-local functionals, defined in Sobolev spaces. Moreover we illustrate some applications for image processing and fracture mechanics.