Monge-Ampere equation on exterior domains

被引：52
作者：
Bao, Jiguang [1 ]
Li, Haigang [1 ]
Zhang, Lei [2 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 52卷 / 1-2期
关键词：
GENERALIZED SOLUTIONS; DIRICHLET PROBLEM; REGULARITY; THEOREM; EXTENSION; BOUNDARY;
D O I：
10.1007/s00526-013-0704-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Monge-AmpSre equation where is a positive function in and for some at infinity. If the equation is globally defined on we classify the asymptotic behavior of solutions at infinity. If the equation is defined outside a convex bounded set we solve the corresponding exterior Dirichlet problem. Finally we prove for the existence of global solutions with prescribed asymptotic behavior at infinity. The assumption is sharp for all the results in this article.
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收藏
页码：39 / 63
页数：25
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