Singular Monge-Ampere equations over convex domains

Electronic Journal of Differential Equations

article

Mengni Li¹ 

[1]Department of Mathematical Sciences and Yau Mathematical Sciences Center Tsinghua University

关键词: Dirichlet problem;    Holder estimate;    bounded convex domain;    unbounded convex domain.;   

DOI  :  10.58997/ejde.2021.86

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article we are interested in the Dirichlet problem for a class of singular Monge-Ampere equations over convex domains being either bounded or unbounded. By constructing a family of sub-solutions, we prove the existence and global Holder estimates of convex solutions to the problem over convex domains. The global regularity provided essentially depends on the convexity of the domain.

【 授权许可】

CC BY