Gradient regularity for a class of elliptic obstacle problems

We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form F (v, ) =_ F (x, Dv) dx, under the constraint v a. e. in, where is a fixed obstacle function. Assuming that the coefficients of the partial map x D_ F (x, ) satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers.