Local Estimates for Minimizers of Some Convex Integral Functional of the Gradient and the Strong Maximum Principle

Abstract

We consider a class of convex integral functionals with lagrangeans depending only on the gradient and satisfying a generalized symmetry assumption, which includes as a particular case the rotational symmetry. Adapting the method by A. Cellina we obtain a kind of local estimates for minimizers in the respective variational problems, which is applied then to deduce some versions of the Strong Maximum Principle in the variational setting.