Regularity results for non-autonomous variational integrals with discontinuous coefficients

We investigate the regularity properties of local minimizers of non autonomous convex integral functionals of the type F(u; Omega) := integral(Omega) f(x,Du)dx, with p-growth into the gradient variable and discontinuous dependence on the x variable. We prove a higher differentiability result for local minimizers of the functional. F(u; Omega) assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space.