Nonconvex variational problems with anisotropic perturbations

We obtain the Γ(L 1 (Ω) - )-limit for a class of variational problems which arise as an «anisotropic» singular perturbation of a nonconvex functional. Any limit of minimizers of the perturbed problems must minimize the new variational problem which arises in the Γ-limit, and the primary goal is to understand the dependence of this new variational problem on the type of perturbation chosen