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 $\mathbb H^n\times \mathbbR^+$.

CINTI E, TAN J. (2016). A nonlinear Liouville theorem for fractional equations in the Heisenberg group. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 433, 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 $\mathbb H^n\times \mathbbR^+$.
2016
CINTI E, TAN J. (2016). A nonlinear Liouville theorem for fractional equations in the Heisenberg group. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 433, 434-454 [10.1016/j.jmaa.2015.07.050].
CINTI E; TAN J.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/599049
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 14
social impact