Green Functions for Sub-Laplacian on Half Spaces of the Heisenberg Group

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Na Wei 1 Pengcheng Niu 1,* Jialin Wang 2

1. Department of Applied Mathematics; Key Laboratory of Space Applied Physics and Chemistry, Ministry of Northwestern Polytechnical University Education Xi’an, Shaanxi Province, 710129, China

2. Key Laboratory of Numerical Simulation Technology of Jiangxi Provinc

* Corresponding author.


Received: 18 Aug. 2011 / Revised: 24 Sep. 2011 / Accepted: 26 Oct. 2011 / Published: 5 Dec. 2011

Index Terms

Heisenberg group, half space, Green function


Green functions for sub-Laplacian on the domains in the Heisenberg group are derived, which can be used to solve partial differential equations subject to specific initial conditions or boundary conditions. Then the integral formulas for sub-Laplace equation on characteristic and non-characteristic half spaces are given, respectively.

Cite This Paper

Na Wei,Pengcheng Niu,Jialin Wang,"Green Functions for Sub-Laplacian on Half Spaces of the Heisenberg Group", IJEM, vol.1, no.6, pp.36-43, 2011. DOI: 10.5815/ijem.2011.06.06


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