Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge-Ampere Equations

被引：17
作者：
Hong, Jiaxing [1 ]
Huang, Genggeng [1 ]
Wang, Weiye [1 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 36卷 / 04期
关键词：
Degenerate ellipticity; Global smooth solutions; Monge-Ampere equations; REGULARITY; CURVATURE;
D O I：
10.1080/03605302.2010.514171
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper the existence of global smooth solutions to the homogeneous Dirichlet problem for degenerate elliptic Monge-Ampere equation: det(uij)=K(x)f(x, u, Du) in a smooth, strictly convex domain < subset of>R2 is proved provided that [image omitted] and [image omitted] positive in and degenerate at finite degree on . Some applications to the regularity of solutions for eigenvalue problem for Monge-Ampere equations is discussed and in two dimensions an affirmative answer to a related problem raised by Trudinger is given.
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收藏
页码：635 / 656
页数：22
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