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.
Fausto Ferrari, Bruno Franchi (2015). Harnack inequality for fractional sub-Laplacians in Carnot groups. MATHEMATISCHE ZEITSCHRIFT, 279(1-2), 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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