C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation-Reference-Cited by-同舟云学术

C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation

Published:2023-09-07 Issue:1 Volume:77 Page:731-794
ISSN:0010-3640
Container-title:Communications on Pure and Applied Mathematics
language:en
Short-container-title:Comm Pure Appl Math

Author:

Chen Shibing¹,Liu Jiakun²,Wang Xu‐Jia³

Affiliation:

1. University of Science and Technology of China Hefei Anhui China

2. University of Wollongong Wollongong New South Wales Australia

3. The Australian National University Canberra Australia

Abstract

AbstractThe regularity of the free boundary in optimal transportation is equivalent to that of the potential function along the free boundary. By establishing new geometric estimates of the free boundary and studying the second boundary value problem of the Monge‐Ampère equation, we obtain the regularity of the potential function as well as that of the free boundary, thereby resolve an open problem raised by Caffarelli and McCann.

Funder

National Key Research and Development Program of China

National Science Fund for Distinguished Young Scholars

National Natural Science Foundation of China

Australian Research Council

Publisher

Wiley

Subject

Applied Mathematics,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/am-pdf/10.1002/cpa.22151

Reference22 articles.

1. Boundary C1,α regularity of potential functions in optimal transportation with quadratic cost

2. The regularity of mappings with a convex potential

3. Boundary regularity of maps with convex potentials

4. Boundary Regularity of Maps with Convex Potentials--II

5. Free boundaries in optimal transport and Monge-Ampère obstacle problems

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