Fractional Laplacians, perimeters and heat semigroups in Carnot groups

Fausto Ferrari; Michele Miranda Jr; Diego Pallara; Andrea Pinamonti; Yannick Sire

doi:10.3934/dcdss.2018026

Article Contents

2018, Volume 11, Issue 3: 477-491. Doi: 10.3934/dcdss.2018026

This issue Previous Article (Non)local and (non)linear free boundary problems Next Article Some remarks on boundary operators of Bessel extensions

Fractional Laplacians, perimeters and heat semigroups in Carnot groups

1.
Dip. di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, 40126, Bologna, Italy
2.
Dip. di Matematica e Informatica, Università di Ferrara, via Machiavelli 30, 44121 Ferrara, Italy
3.
Dip. di Matematica e Fisica "Ennio De Giorgi", Università del Salento, P.O.B. 193, and INFN, 73100 Lecce, Italy
4.
Dip. di Matematica, Università di Trento, via Sommarive, 14, 38123 Povo (TN), Italy
5.
Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, Baltimore, MD 21218, USA

* Corresponding author.
* Corresponding author.

Received: April 30, 2017

Revised: July 31, 2017

Published: June 2018

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Abstract

We define and study the fractional Laplacian and the fractional perimeter of a set in Carnot groups and we compare the perimeter with the asymptotic behaviour of the fractional heat semigroup.

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Mathematics Subject Classification: Primary: 35C15, 35J15; Secondary: 35K08.

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