Strong maximum principle for generalized solutions to equations of the Monge-Ampère type ☆

被引：0

作者：

Jian, Huaiyu ^{[1
]}

Tu, Xushan ^{[2
]}

机构：

[1] Beijing Technol & Business Univ, Sch Math & Stat, Beijing, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2025年 / 463卷

关键词：

Strong maximum principle; Monge-Amp & egrave; re equation; Strict convexity; Uniqueness; P-MINKOWSKI PROBLEM; MONGE-AMPERE; REGULARITY;

D O I：

10.1016/j.aim.2025.110116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Amp & egrave;re type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily C 1 , 1 smooth, and show that it fails at non-strictly convex points. The results we obtain can be applied to various Minkowski type problems in convex geometry by the virtue of the Gauss image map. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：39

共 41 条

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