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 [8], as established in [14]. 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 ℍn × ℝ+.
@article{5289,
title = {A Liouville Theorem for Nonlocal Equations in the Heisenberg Group},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2014},
doi = {10.6092/issn.2240-2829/5289},
language = {EN},
url = {http://dml.mathdoc.fr/item/5289}
}
Cinti, Eleonora. A Liouville Theorem for Nonlocal Equations in the Heisenberg Group. Bruno Pini Mathematical Analysis Seminar, (2014), . doi : 10.6092/issn.2240-2829/5289. http://gdmltest.u-ga.fr/item/5289/