Harnack inequality for fractional sub-Laplacians in Carnot groups
By Fausto Ferrari, Bruno Franchi. 2012
85 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/b4058aab8b122c747eb31a4d30afaa990a8ece65
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In Applied Mathematics
- Jinggang Tan
- Mar'ia de Mar Gonz'alez
- D. Monticelli
- Rupert L. Frank
- Fausto Ferrari
- M. Fall
- Enrico Valdinoci
- Raffaella Servadei
In Computational Theory and Mathematics
- Mar'ia de Mar Gonz'alez
- Jinggang Tan
- Rupert L. Frank
- D. Monticelli
- Fausto Ferrari
- Raffaella Servadei
- M. Fall
- Giovanni Molica Bisci
Citations in the corpus
- An extension problem for the CR fractional Laplacian (2013, methodology): “ of the extra direction. Using functional analysis tools, one may formulate an extension problem to construct the pure fractional powers of the sub–Laplacian on Carnot groups (see the related work of [25] and [57]). An interesting feature of our point of view is that one needs to use the 1 2 R. L. F”
- Weyl and Marchaud Derivatives: A Forgotten History (2017, methodology): “[5] for facing the case of the semigroup approach in its abstract generality and then for recalling the contribution given in [58], for fractional Laplace operators, and then recalling [30] for several generalizations in an abstract approach, including in principle: Riemannian manifolds, Lie groups,”