Global regularity of optimal mappings in non-convex domains

Shibing Chen; Jiakun Liu; Xu Jia Wang

doi:10.1007/s11425-018-9465-8

Global regularity of optimal mappings in non-convex domains

Shibing Chen, Jiakun Liu, Xu Jia Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.

Original language	English
Pages (from-to)	2057-2072
Number of pages	16
Journal	Science China Mathematics
Volume	62
Issue number	11
DOIs	https://doi.org/10.1007/s11425-018-9465-8
Publication status	Published - 1 Nov 2019

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title = "Global regularity of optimal mappings in non-convex domains",

abstract = "In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.",

keywords = "35B65, 35J25, 35J96, Monge-Amp{\`e}re equation, global regularity, optimal transportation",

author = "Shibing Chen and Jiakun Liu and Wang, {Xu Jia}",

note = "Publisher Copyright: {\textcopyright} 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

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T1 - Global regularity of optimal mappings in non-convex domains

AU - Chen, Shibing

AU - Liu, Jiakun

AU - Wang, Xu Jia

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.

AB - In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.

KW - 35B65

KW - 35J25

KW - 35J96

KW - Monge-Ampère equation

KW - global regularity

KW - optimal transportation

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U2 - 10.1007/s11425-018-9465-8

DO - 10.1007/s11425-018-9465-8

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VL - 62

SP - 2057

EP - 2072

JO - Science China Mathematics

JF - Science China Mathematics

IS - 11

ER -

Global regularity of optimal mappings in non-convex domains

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