Singular solutions of fractional order conformal Laplacians

TL;DR

This paper studies the behavior of solutions to fractional conformal Laplacians, aiming to extend known properties of singular solutions from classical Yamabe problems to fractional orders.

Contribution

It introduces a framework for analyzing singular solutions of fractional conformally covariant elliptic operators, generalizing classical results in the Yamabe problem.

Findings

Characterization of singular sets for fractional conformal Laplacians

Extension of classical Yamabe solution properties to fractional order

New analytical tools for fractional elliptic operators

Abstract

We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.