A Liouville type theorem to an extension problem relating to the Heisenberg group

Xinjing Wang; Pengcheng Niu; Xuewei Cui

doi:10.3934/cpaa.2018113

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2018, Volume 17, Issue 6: 2379-2394. Doi: 10.3934/cpaa.2018113

This issue Previous Article The spectral expansion approach to index transforms and connections with the theory of diffusion processes Next Article An inhomogeneous evolution equation involving the normalized infinity Laplacian with a transport term

A Liouville type theorem to an extension problem relating to the Heisenberg group

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710129, China

* Corresponding author
* Corresponding author

Received: May 31, 2017

Revised: December 31, 2017

Published: June 2018

This work is supported by the Natural Science Basic Research plan in Shaanxi Province of China (Grant No. 2016JM1023). The first author partially supported by NSFC (Grant No. 11471188 & 11771354) and the National Science Foundation for Young Scientists of China (Grant No. 11601427).

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We establish a Liouville type theorem for nonnegative cylindrical solutions to the extension problem corresponding to a fractional CR covariant equation on the Heisenberg group by using the generalized CR inversion and the moving plane method.

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Mathematics Subject Classification: 35A01, 35J57, 35D99.

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