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, as established in \cite{FGMT}. 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 $\mathbb H^n\times \mathbbR^+$.
A nonlinear Liouville theorem for fractional equations in the Heisenberg group / CINTI E; TAN J.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 433:(2016), pp. 434-454. [10.1016/j.jmaa.2015.07.050]
A nonlinear Liouville theorem for fractional equations in the Heisenberg group
CINTI, ELEONORA;
2016
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, as established in \cite{FGMT}. 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 $\mathbb H^n\times \mathbbR^+$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.