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.
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页数：18
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