In this paper we prove a higher differentiability result for the solutions to a class of obstacle problems in the form \begin{ equation*} \label{ obst-def0} \min\left\{ \int_\Omega F(x,Dw) dx : w\in \mathcal{ K}_{ \psi}(\Omega)\right\} \end{ equation*} where $\psi\in W^{ 1,p(x)}(\Omega)$ is a fixed function called obstacle and $\mathcal{ K}_{ \psi}=\{ w \in W^{ 1,p(x)}_{ 0}(\Omega)+u_0: w \ge \psi \,\, \textnormal{ a.e. in $\Omega$}\}$ is the class of the admissible functions, for a suitable boundary value $ u_0 $. We deal with a convex integrand $F$ which satisfies the $p(x)$-growth conditions \begin{ equation*}\label{ growth}|\xi|^{ p(x)}\le F(x,\xi)\le C(1+|\xi|^{ p(x)}),\quad p(x)>1 \end{ equation*}
Categories: math.AP