Boundary C1,α regularity of an optimal transport problem with cost close to -X · Y

Shibing Chen

doi:10.1137/140993089

Boundary C^1,α regularity of an optimal transport problem with cost close to -X · Y

Shibing Chen^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We prove that optimal transport maps between positive continuous densities supported on C² uniformly convex domains are C^α up to the boundary, provided that the cost function is a sufficiently small perturbation of the quadratic cost -x · y.

Original language	English
Pages (from-to)	2689-2698
Number of pages	10
Journal	SIAM Journal on Mathematical Analysis
Volume	47
Issue number	4
DOIs	https://doi.org/10.1137/140993089
Publication status	Published - 2015

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title = "Boundary C1,α regularity of an optimal transport problem with cost close to -X · Y",

abstract = "We prove that optimal transport maps between positive continuous densities supported on C2 uniformly convex domains are Cα up to the boundary, provided that the cost function is a sufficiently small perturbation of the quadratic cost -x · y.",

keywords = "Boundary regularity, Holder regularity, Optimal transport, Perturbation",

author = "Shibing Chen",

note = "Publisher Copyright: {\textcopyright} 2015 Society for Industrial and Applied Mathematics.",

year = "2015",

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language = "English",

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pages = "2689--2698",

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T1 - Boundary C1,α regularity of an optimal transport problem with cost close to -X · Y

AU - Chen, Shibing

PY - 2015

Y1 - 2015

N2 - We prove that optimal transport maps between positive continuous densities supported on C2 uniformly convex domains are Cα up to the boundary, provided that the cost function is a sufficiently small perturbation of the quadratic cost -x · y.

AB - We prove that optimal transport maps between positive continuous densities supported on C2 uniformly convex domains are Cα up to the boundary, provided that the cost function is a sufficiently small perturbation of the quadratic cost -x · y.

KW - Boundary regularity

KW - Holder regularity

KW - Optimal transport

KW - Perturbation

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U2 - 10.1137/140993089

DO - 10.1137/140993089

M3 - Article

SN - 0036-1410

VL - 47

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EP - 2698

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Boundary C^1,α regularity of an optimal transport problem with cost close to -X · Y

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