Higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients

We study the local regularity of vectorial minimizers of integral functionals with standard p-growth. We assume that the non-homogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. Under a W1,n-Sobolev dependence on the spatial variable of the integrand, n being the space dimension, we show that the minimizers have the gradient locally in Lq for every q>p. As a consequence, they are locally α-Hölder continuous for every α<1.