Mean value properties  of  fractional second order operators

Fausto Ferrari

doi:10.3934/cpaa.2015.14.83

Article Contents

2015, Volume 14, Issue 1: 83-106. Doi: 10.3934/cpaa.2015.14.83

This issue Previous Article On a conjectured reverse Faber-Krahn inequality for a Steklov--type Laplacian eigenvalue Next Article Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation

Mean value properties of fractional second order operators

Fausto Ferrari^1,

1.
Dipartimento di Matematica dell'Università di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna

Received: February 2014

Revised: April 2014

Published: January 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we introduce a method to define fractional operators using mean value operators. In particular we discuss a geometric approach in order to construct fractional operators. As a byproduct we define fractional linear operators in Carnot groups, moreover we adapt our technique to define some nonlinear fractional operators associated with the $p-$Laplace operators in Carnot groups.

Keywords:

Mathematics Subject Classification: Primary: 35H20, 35J60; Secondary: 35E05, 35J92.

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