Regularity for non convex functionals with p − q growth via relaxations methods

We prove the local Lipschitz continuity for local minimizers of vectorial integrals with density energy, which depends on the space variable, satisfies p-q growth condition and it is not convex with respect to the gradient. In particular the radial structure condition and the uniform convexity with respect to the last variable, are assumed only at infinity. The arguments of the proof are new and based on some relaxation results for functionals with nonstandard growth.