A nonlinear Liouville theorem for fractional equations in the Heisenberg group

Abstract

We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the subLaplacian 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 [9], as established in [16]. 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+.