期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 477, 期 2, 页码 1072-1086出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.04.075
关键词
Prescribed constant mean curvature equation; Critical point; Uniqueness; Non-degeneracy
资金
- National Natural Science Foundation of China [11401307, 11401310]
- High Level Talent Research Fund of Nanjing Forestry University [02014022]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province [NYCX17_0321]
- China Scholarship Council (CSC) [201806840122]
In this paper, we investigate the critical points of solutions to the prescribed constant mean curvature equation with Neumann and Robin boundary conditions respectively in a bounded smooth convex domain Omega of R-n (n >= 2). Firstly, we show the non-degeneracy and uniqueness of the critical points of solutions in a planar domain by using the local Chen & Huang's comparison technique and the geometric properties of approximate surfaces at the non-degenerate critical points. Secondly, we deduce the uniqueness and non-degeneracy of the critical points of solutions in a rotationally symmetric domain of R-n (n >= 3) by the projection of higher dimensional space onto two dimensional plane. (C) 2019 Elsevier Inc. All rights reserved.
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