Higher differentiability of minimizers of convex variational integrals

Abstract

In this paper we consider integral functionals of the formF(v,Ω)=∫ΩF(Dv(x))dx with convex integrand satisfying (p,q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents.As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand.