Seminari del Dipartimento di Matematica

Seminario del 2014

A Liouville-type Theorem for a nonlinear and nonlocal problem in the Heisenberg group.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

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 $\mathbb{H}^n\times \R^+$. This is a joint work with Jinggang Tan.