# SUBGRADIENT ESTIMATES FOR A NONLINEAR SUBELLIPTIC EQUATION ON COMPLETE PSEUDOHERMITIAN MANIFOLD

• Han, Yingbo (School of Mathematics and Statistics Xinyang Normal University) ;
• Jiang, Kaige (School of Mathematics and Statistics Xinyang Normal University) ;
• Liang, Mingheng (King's College London)
• Accepted : 2017.03.31
• Published : 2018.01.31

#### Abstract

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

#### Acknowledgement

Supported by : National Natural Science Foundation of China, China Scholarship Council, XYNU

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