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Gradient estimates of mean curvature equations with semi-linear oblique boundary value problems


Authors: Jinju Xu and Lu Xu
Journal: Proc. Amer. Math. Soc. 145 (2017), 3481-3491
MSC (2010): Primary 35B45; Secondary 35J92, 35B50
DOI: https://doi.org/10.1090/proc/13483
Published electronically: January 31, 2017
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Abstract: In this paper, we consider the semi-linear oblique boundary value problem for the prescribed mean curvature equation. We find a suitable auxiliary function and use the maximum principle to get the gradient estimate. As a consequence, we obtain the corresponding existence theorem for a class of mean curvature equations with semi-linear oblique derivative problems.


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Additional Information

Jinju Xu
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234 People’s Republic of China – and – Department of Mathematics, Shanghai University, Shanghai 200444 People’s Republic of China
Email: jjxujane@shu.edu.cn

Lu Xu
Affiliation: Institute of Mathematics, Hunan University, Changsha 410082 People’s Republic of China
Email: xulu@hnu.edu.cn

DOI: https://doi.org/10.1090/proc/13483
Keywords: Gradient estimate, oblique boundary value, maximum principle
Received by editor(s): February 27, 2016
Received by editor(s) in revised form: September 15, 2016
Published electronically: January 31, 2017
Additional Notes: The research of the first author was supported by NSFC No.11601311, and the research of the second author was supported by NSFC No.11371360.
Communicated by: Guofang Wei
Article copyright: © Copyright 2017 American Mathematical Society