Regularity of optimal mapping between hypercubes-Reference-Cited by-同舟云学术

Regularity of optimal mapping between hypercubes

Published:2023-01-01 Issue:1 Volume:23 Page:
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Chen Shibing¹,Liu Jiakun²,Wang Xu-Jia³

Affiliation:

1. School of Mathematical Sciences, University of Science and Technology of China , Hefei , 230026 , P.R. China

2. School of Mathematics and Applied Statistics, University of Wollongong , Wollongong , NSW 2522 , Australia

3. Centre for Mathematics and Its Applications, The Australian National University , Canberra, ACT 0200 , Australia

Abstract

Abstract In this note, we establish the global

C 3 , α

{C}^{3,\alpha }

regularity for potential functions in optimal transportation between hypercubes in

R n

{{\mathbb{R}}}^{n}

for

n ≥ 3

n\ge 3

. When

n = 2

n=2

, the result was proved by Jhaveri. The

C 3 , α

{C}^{3,\alpha }

regularity is also optimal due to a counterexample in the study by Jhaveri.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2023-0087/pdf

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