# A NONLINEAR LIOUVILLE THEOREM FOR FRACTIONAL EQUATIONS IN THE HEISENBERG GROUP

created by cinti on 27 Jun 2014
modified on 02 Sep 2015

[BibTeX]

Accepted Paper

Inserted: 27 jun 2014
Last Updated: 2 sep 2015

Journal: Journal of Math. Analysis and Appl.
Year: 2014

Abstract:

We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space $\mathbb H^n\times \mathbb R^+$.