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,Ω)=∫_Ω F(x,Dv)dx, under the constraint v ≥ ψ a.e. in Ω, where ψ is a fixed obstacle function. Assuming that the coefficients of the partial map x ↦ D_ξ F(x,ξ) satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers.