English

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}
}