Bulletin of the
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Bull. Korean Math. Soc. 2018; 55(1): 175-186

Online first article July 28, 2017      Printed January 31, 2018

https://doi.org/10.4134/BKMS.b160922

Copyright © The Korean Mathematical Society.

Subgradient estimates for a nonlinear subelliptic equation on complete pseudohermitian manifold

Yingbo Han, Kaige Jiang, Mingheng Liang

Xinyang Normal University, Xinyang Normal University,

Abstract

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

Keywords: subgradient estimate, nonlinear subparabolic equation, pseudohermitian manifold

MSC numbers: 32V05, 32V20

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