Regularity results for a class of obstacle problems with $p,q-$growth conditions

In this paper we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $$\min \{{\int }_{\mathrm{\Omega }}F(x,Dz):z\in {\mathcal{K}}_{\psi }(\mathrm{\Omega })\}\mathrm{.}$$ Here ${\mathcal{K}}_{\psi }(\mathrm{\Omega })$ is set of admissible functions $z \in W^{1,p}(\Omega)$suchthat$z \ge \psi$a\mathrm{.}e\mathrm{.}in$\Omega$,$\psi$ being the obstacle and $\mathrm{\Omega }$ being an open bounded set of ${\mathbb{R}}^n$, $n\ge 2$. The main novelty here is that we are assuming $F(x,Dz)$ satisfying $(p,q)$-growth conditions {and less restrictive assumptions on the obstacle with respect to the existing regularity results}.