Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 86, pp. 1-18.

Title: Singular Monge-Ampere equations over convex domains
       
Author: Mengni Li (Tsinghua Univ., Beijing 100084, China)

Abstract:
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.

Submitted November 26, 2020. Published October 18, 2021.
Math Subject Classifications: 35J96, 52A20, 35B65.
Key Words: Dirichlet problem; Holder estimate; bounded convex domain;
           unbounded convex domain.