Title

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

Publication Name

Annals of Mathematics

Abstract

In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u= f subject to boundary condition Du(Ω)= Ω*, where Ω and Ω* are bounded convex domains in the Euclidean space Rn with C1,1 boundaries, and f is a Hölder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications

Open Access Status

This publication may be available as open access

Volume

194

Issue

3

First Page

745

Last Page

793

Funding Number

DP170100929

Funding Sponsor

Australian Research Council

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Link to publisher version (DOI)

http://dx.doi.org/10.4007/annals.2021.194.3.4