Harnack inequality for fractional sub-Laplacians in Carnot groups

Abstract

In this paper we prove an invariant Harnack inequality on Carnot-Carathéodory 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.

References in corpus (2)

• An extension problem related to the fractional Laplacian
• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

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