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In this paper we prove a higher differentiability result for the solutions toa 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 $\psi\inW^{1,p(x)}(\Omega)$ 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, fora suitable boundary value $ u_0 $. We deal with a convex integrand $F$ whichsatisfies the $p(x)$-growth conditions\begin{equation*}\label{growth}|\xi|^{p(x)}\le F(x,\xi)\leC(1+|\xi|^{p(x)}),\quad p(x)>1 \end{equation*}

Higher differentiability of solutions for a class of obstacle problems with variable exponents