An extremal property of the inf- and sup- convolutions regarding the Strong Maximum Principle

Abstract

In this paper we continue investigations started in the paper "Local estimates for minimizers of some convex integral functional of the gradient and the Strong Maximum Principle" concerning the extension of the variational Strong Maximum Principle for lagrangeans depending on the gradient through a Minkowski gauge. We essentially enlarge the class of comparison functions, which substitute the identical zero when the lagrangean is not longer strictly convex at the origin.