Singular Monge-Ampere equations over convex domains
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Date
2021-10-18
Authors
Li, Mengni
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we are interested in the Dirichlet problem for a class of singular Monge-Ampère equations over convex domains being either bounded or unbounded. By constructing a family of sub-solutions, we prove the existence and global Hölder estimates of convex solutions to the problem over convex domains. The global regularity provided essentially depends on the convexity of the domain.
Description
Keywords
Dirichlet problem, Hölder estimate, Bounded convex domain, Unbounded convex domain
Citation
Li, M. (2021). Singular Monge-Ampere equations over convex domains. <i>Electronic Journal of Differential Equations, 2021</i>(86), pp. 1-18.