Regularity results for minimizers of non-autonomous integral functionals

Abstract We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{align*} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \end{align*} under ( p , q )-growth conditions. Besides a suitable differentiability assumption on the partial map $x \mapsto D_\xi f(x,\xi)$ , we do not need to assume any differentiability assumption on the function g .