Regularity of optimal mapping between hypercubes

Authors

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

Publication Name

Advanced Nonlinear Studies

Abstract

In this note, we establish the global C3,α regularity for potential functions in optimal transportation between hypercubes in ℝn for n ≥ 3. When n = 2, the result was proved by Jhaveri. The C3,α regularity is also optimal due to a counterexample in the study by Jhaveri.

Open Access Status

This publication may be available as open access

Volume

23

Issue

1

Article Number

20230087

Funding Number

DP200101084

Funding Sponsor

Australian Research Council