Liouville Theorems for a Class of Degenerate or Singular Monge-Ampère Equations

被引：0

作者：

Wang, Ling ^{[1
]}

Zhou, Bin ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 11期

基金：

国家重点研发计划;

关键词：

Degenerate Monge-Amp & egrave; re equation; Liouville theorems; Partial Legendre transform; Method of moving spheres; MONGE-AMPERE EQUATIONS; BOUNDARY-REGULARITY; EXTENSION;

D O I：

10.1007/s12220-024-01795-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we classify solutions to a class of Monge-Amp & egrave;re equations whose right hand side may be degenerate or singular in the half space. Solutions to these equations are special solutions to a class of fourth order equations, including the affine maximal hypersurface equation, in the half space. Both the Dirichlet boundary value and Neumann boundary value cases are considered.

引用

页数：18

共 31 条

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