Stability of Edelen-Wang?s Bernstein type theorem for the minimal surface equation

被引：0
|
作者：
Jiang, Guosheng [1 ]
Wang, Zhehui [2 ]
Zhu, Jintian [3 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, MOE, Beijing 100875, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[3] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2023年 / 284卷 / 06期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Stability; Bernstein type theorem; Minimal surface equation; Unbounded convex domain; DIRICHLET PROBLEM; REGULARITY;
D O I：
10.1016/j.jfa.2022.109821
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let 12 C Rn (n >= 2) be an unbounded convex domain. We study the minimal surface equation in 12 with boundary value given by the sum of a linear function and a bounded uniformly continuous function in Rn. If 12 is not a half space, we prove that the solution is unique. If 12 is a half space, we prove that graphs of all solutions form a foliation of 12 x R. This can be viewed as a stability type theorem for Edelen-Wang's Bernstein type theorem in [10]. We also establish a comparison principle for the minimal surface equation in 12. (c) 2022 Elsevier Inc. All rights reserved.
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页数：27
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