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.
@article{2668,
title = {Some relations between fractional Laplace operators and Hessian operators},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2011},
doi = {10.6092/issn.2240-2829/2668},
language = {EN},
url = {http://dml.mathdoc.fr/item/2668}
}
Ferrari, Fausto. Some relations between fractional Laplace operators and Hessian operators. Bruno Pini Mathematical Analysis Seminar, (2011), . doi : 10.6092/issn.2240-2829/2668. http://gdmltest.u-ga.fr/item/2668/