Inserted: 19 feb 2008
Last Updated: 10 nov 2008
Journal: Math. Meth. Appl. Sci.
We approximate, in the sense of $\Gamma$-convergence, free discontinuity functionals with linear growth by a sequence of non local integral functionals depending on the average of the gradient on small balls. The result extends to higher dimension what already proved in the one-dimensional case, and in the n-dimensional case with the some restrictions on absolutely continuous part of the $\Gamma$-limit. Moreover we investigate wether it is possible to approximate a given free discontinuity functional by means of non-local energies.