A singular Monge-Ampère equation on unbounded domains

被引：1

作者：

Huaiyu Jian ^{[1
]}

You Li ^{[1
]}

机构：

[1] Department of Mathematical Sciences, Tsinghua University

来源：

ScienceChina(Mathematics) | 2018年 / 61卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Dirichlet problem; singular Monge-Amp`ere equation; unbounded domain;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we study the Dirichlet problem for a singular Monge-Amp`ere type equation on unbounded domains. For a few special kinds of unbounded convex domains, we find the explicit formulas of the solutions to the problem. For general unbounded convex domain ?, we prove the existence for solutions to the problem in the space C∞(?) ∩ C(?). We also obtain the local C1/2-estimate up to the ?? and the estimate for the lower bound of the solutions.

引用

页码：1473 / 1480

页数：8

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