Higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients. (May 2017) - Cupini, Giovanni; Giannetti, Flavia; Giova, Raffaella; Passarelli di Napoli, Antonia
Abstract: 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 W 1, 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 L q for every q > p . As a consequence, they are locally α -Hölder continuous for every α < 1 .