Global regularity for the Monge-Ampère equation with natural boundary condition

2018/02/21 by Chen, Shibing, Liu, Jiakun, Wang, Xu-Jia · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.07518

Abstract

In this paper, we establish the global C^2,α and W^2,p regularity for the Monge-Ampère equation det D²u = f subject to boundary condition Du(Ω) = Ω^*, where Ω and Ω^* are bounded convex domains in the Euclidean space ℝⁿ with C^1,1 boundaries, and f is a Hölder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications.

Cited by

• Geometric invariants and the Monge-Ampere equation in Kähler geometry
• Homogeneous optimal transport maps between oblique cones
• Boundary regularity of optimal transport maps on convex domains

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