A Liouville Theorem for Nonlocal Equations in the Heisenberg Group

A Liouville Theorem for Nonlocal Equations in the Heisenberg Group

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 opera...

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Main Author: Eleonora Cinti
Format: Article
Language:English
Published: University of Bologna 2014-12-01
Series:Bruno Pini Mathematical Analysis Seminar
Subjects:
Fractional sublaplacian
Heisenberg group
Louville theorem
moving plane method
Online Access:http://mathematicalanalysis.unibo.it/article/view/5289
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spelling doaj-37b2c77486b843b2ba3b7406054618ae2020-11-25T00:21:00ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292014-12-015112714610.6092/issn.2240-2829/52894846A Liouville Theorem for Nonlocal Equations in the Heisenberg GroupEleonora Cinti0Weierstrass Institute for Applied Analysis and StochasticsWe 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+.http://mathematicalanalysis.unibo.it/article/view/5289Fractional sublaplacianHeisenberg groupLouville theoremmoving plane method
collection DOAJ
language English
format Article
sources DOAJ
author Eleonora Cinti
spellingShingle Eleonora Cinti
A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
Bruno Pini Mathematical Analysis Seminar
Fractional sublaplacian
Heisenberg group
Louville theorem
moving plane method
author_facet Eleonora Cinti
author_sort Eleonora Cinti
title A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
title_short A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
title_full A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
title_fullStr A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
title_full_unstemmed A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
title_sort liouville theorem for nonlocal equations in the heisenberg group
publisher University of Bologna
series Bruno Pini Mathematical Analysis Seminar
issn 2240-2829
publishDate 2014-12-01
description 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+.
topic Fractional sublaplacian
Heisenberg group
Louville theorem
moving plane method
url http://mathematicalanalysis.unibo.it/article/view/5289
work_keys_str_mv AT eleonoracinti aliouvilletheoremfornonlocalequationsintheheisenberggroup
AT eleonoracinti liouvilletheoremfornonlocalequationsintheheisenberggroup
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