Regularity results for non-autonomous variational integrals with discontinuous coefficients

Abstract

We investigate the regularity propertiesof local minimizers of non autonomous convex integral functionals of the type

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 $\mathcal{F}(u;\Omega )$ assuming that the function that measures the oscillation of the integrand with respect to the $x$ variable belongs to a suitable Sobolev space.