Abstract We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form align* F (u, ): =_ f (x, Du) - g u dx, align* under (p, q) -growth conditions. Besides a suitable differentiability assumption on the partial map x D_ f (x, ), we do not need to assume any differentiability assumption on the function g.
Grimaldi et al. (Fri,) studied this question.