Harnack inequality for fractional sub-Laplacians in Carnot groups
Analysis of PDEs
2014-09-19 v4
Abstract
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups.
Keywords
Cite
@article{arxiv.1206.0885,
title = {Harnack inequality for fractional sub-Laplacians in Carnot groups},
author = {Fausto Ferrari and Bruno Franchi},
journal= {arXiv preprint arXiv:1206.0885},
year = {2014}
}