Local estimates for functionals rotationally invariant with respect to the gradient

Abstract

This paper concerns minimization problems from Calculus of Variations rotationally invariant with respect to the gradient. Inspired by properties associated with results which are valid for elliptic partial differential equations, it presents some local estimates nearby non extremum points as well as nearby extremum points for these problems, generalizing some results obtained by Arrigo Cellina, Vladimir V. Goncharov and myself. As a consequence, some local estimates are obtained for the difference between the supremum and the infimum of any solution to the problem considered