A Liouville Theorem for Nonlocal Equations in the Heisenberg Group

Eleonora Cinti

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 [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+.

Keywords


Fractional sublaplacian; Heisenberg group; Louville theorem; moving plane method

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References


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DOI: 10.6092/issn.2240-2829/5289

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