Regularity results for non-autonomous variational integrals with discontinuous coefficients

We investigate the regularity propertiesof local minimizers of non autonomous convex integral functionals of the type F(u; Ω):= ∫Ω 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; Ω) assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space.