Regularity results for non-autonomous variational integrals with discontinuous coefficients (Q900708)

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