Fractional Laplacians and extension problems: the higher rank case

2016/09/28 by Gonzalez, Maria del Mar, Saez, Mariel
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.09151

Abstract

The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetric spaces and, second, we construct new boundary operators with good conformal properties that generalize the fractional Laplacian using an extension problem in which the boundary is of codimension two.

Related

• Fractional Laplacian in Conformal Geometry
• The s-polyharmonic extension problem and higher-order fractional Laplacians
• Recent progress on the fractional Laplacian in conformal geometry
• Hölder extension for fractional Laplacian
• On higher order extensions for the fractional Laplacian