Constant mean curvature surfaces and mean curvature flow with non-zero Neumann boundary conditions on strictly convex domains

被引：49

作者：

Ma, Xi-Nan ^{[1
]}

Wang, Pei-He ^{[2
]}

Wei, Wei ^{[1
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 274卷 / 01期

关键词：

Neumann boundary; Asymptotic behavior; Mean curvature equation; Additive eigenvalue problem; HAMILTON-JACOBI EQUATIONS; EXISTENCE;

D O I：

10.1016/j.jfa.2017.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study nonparametric surfaces over strictly convex bounded domains in R-n, which are evolving by the mean curvature flow with Neumann boundary value. We prove that solutions converge to the ones moving only by translation. And we will prove the existence and uniqueness of the constant mean curvature equation with Neumann boundary value on strictly convex bounded domains. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：252 / 277

页数：26

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