A nonlinear Liouville theorem for fractional equations in the Heisenberg group

作者：Cinti Eleonora; Tan Jinggang^*

来源：Journal of Mathematical Analysis and Applications, 2016, 433(1): 434-454.

DOI：10.1016/j.jmaa.2015.07.050

• Fractional sublaplacian
• Heisenberg group
• Liouville theorem
• Moving plane method

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 [15]. 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 H-n X R+.

• 出版日期2016-1-1