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arXiv · 1504.03122

A nonlinear Liouville theorem for fractional equations in the Heisenberg group

Eleonora Cinti·Jinggang Tan
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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 $\mathbb H^n\times \mathbbR^+$.

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Eleonora Cinti, Jinggang Tan. 2015-04-13. A nonlinear Liouville theorem for fractional equations in the Heisenberg group. https://arxiv.org/abs/1504.03122

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