Boundary ε-regularity in optimal transportation

Shibing Chen; Alessio Figalli

doi:10.1016/j.aim.2014.12.032

Boundary ε-regularity in optimal transportation

Shibing Chen^*, Alessio Figalli

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

We develop an ε-regularity theory at the boundary for a general class of Monge-Ampère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C² uniformly convex domains are C^1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost -x y.

Original language	English
Pages (from-to)	540-567
Number of pages	28
Journal	Advances in Mathematics
Volume	273
DOIs	https://doi.org/10.1016/j.aim.2014.12.032
Publication status	Published - 9 Mar 2015

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10.1016/j.aim.2014.12.032

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title = "Boundary ε-regularity in optimal transportation",

abstract = "We develop an ε-regularity theory at the boundary for a general class of Monge-Amp{\`e}re type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H{\"o}lder densities supported on C2 uniformly convex domains are C1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost -x y.",

keywords = "Boundary regularity, General cost, Monge-Amp{\`e}re, Optimal transportation",

author = "Shibing Chen and Alessio Figalli",

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T1 - Boundary ε-regularity in optimal transportation

AU - Chen, Shibing

AU - Figalli, Alessio

PY - 2015/3/9

Y1 - 2015/3/9

N2 - We develop an ε-regularity theory at the boundary for a general class of Monge-Ampère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C2 uniformly convex domains are C1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost -x y.

AB - We develop an ε-regularity theory at the boundary for a general class of Monge-Ampère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C2 uniformly convex domains are C1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost -x y.

KW - Boundary regularity

KW - General cost

KW - Monge-Ampère

KW - Optimal transportation

UR - https://www.scopus.com/pages/publications/84921472124

U2 - 10.1016/j.aim.2014.12.032

DO - 10.1016/j.aim.2014.12.032

M3 - Article

SN - 0001-8708

VL - 273

SP - 540

EP - 567

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Boundary ε-regularity in optimal transportation

Abstract

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