Some relations between fractional Laplace operators and Hessian operators

Abstract

After recalling the many representations of the fractional Laplace operator and some of its important properties, some recent results (proved in a joint work with Bruno Franchi and Igor Verbitsky) about the relations between the k-Hessian energy of the k-Hessian operator of a k convex function vanishing at infinity and the fractional energy of a particular fractional operator will be introduced. Moreover we shall recall an integration by parts formula for the fractional Laplace operator giving a new simpler proof.