Higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions

Abstract We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. deal case in which satisfy variational inequality form ∫ Ω stretchy="false">⟨ mathvariant="script">A ⁢ stretchy="false">( x , D u stretchy="false">) φ - rspace="4.2pt" stretchy="false">⟩ mathvariant="italic" rspace="0pt">d ≥ 0 separator="true"> for all ∈ mathvariant="script">K ψ \int_{\Omega}\langle\mathcal{A}(x,Du),D(\varphi-u)\rangle\,dx\geq 0\quad\text{for all}\ \varphi\in\mathcal{K}_{\psi}(\Omega), where Ω is bounded open subset mathvariant="double-struck">R n \mathbb{R}^{n} , W 1 p \psi\in W^{1,p}(\Omega) fixed function called and = stretchy="false">{ w : a.e. in stretchy="false">} \mathcal{K}_{\psi}(\Omega)=\{w\in W^{1,p}(\Omega):w\geq\psi\ \text{a.e. in}\ \Omega\} admissible functions. Assuming that gradient belongs some suitable Besov space, we are able prove property transfers solution.