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

Authors

Shibing Chen, University of Science and Technology of China
Jiakun Liu, University of Wollongong
Xu Jia Wang, The Australian National University

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