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