Regular approximation of free-discontinuity problems

We consider a dares of smooth local nonconvex functionals defined on W-2,W- 2(Omega), depending on a small parameter epsilon and we prove that they con verge, as epsilon tends to 0, to a functional F(u, Omega) with a bulk densi ty depending on the gradient of u and a surface energy concentrated on the jump set of u. This provides a new alternative to the approximation of free discontinuity problems, which applies in particular to the Mumford-Shah mo del.