Inserted: 5 jan 2006
Last Updated: 19 feb 2008
Journal: ESAIM Control Optim. Calc. Var.
We approximate, in the sense of $\Gamma$-convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.