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.
Harnack inequality for fractional sub-Laplacians in Carnot groups / Fausto Ferrari; Bruno Franchi. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 279:1-2(2015), pp. 435-458. [10.1007/s00209-014-1376-5]
Harnack inequality for fractional sub-Laplacians in Carnot groups
FERRARI, FAUSTO;FRANCHI, BRUNO
2015
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.File in questo prodotto:
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