Electron. J. Differential Equations, Vol. 2021 (2021), No. 86, pp. 1-18.

Singular Monge-Ampere equations over convex domains

Mengni Li

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.

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Mengni Li
Department of Mathematical Sciences and
Yau Mathematical Sciences Center
Tsinghua University, Beijing 100084, China
email: krisymengni@163.com

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