Stability results on the smoothness of optimal transport maps with general costs

Shibing Chen; Alessio Figalli

doi:10.1016/j.matpur.2016.02.010

Stability results on the smoothness of optimal transport maps with general costs

Shibing Chen, Alessio Figalli^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We prove some stability results concerning the smoothness of optimal transport maps with general cost functions. In particular, we show that the smoothness of optimal transport maps is an open condition with respect to the cost function and the densities. As a consequence, we obtain regularity for a large class of transport problems, where the cost does not necessarily satisfy the MTW condition.

Original language	English
Pages (from-to)	280-295
Number of pages	16
Journal	Journal des Mathematiques Pures et Appliquees
Volume	106
Issue number	2
DOIs	https://doi.org/10.1016/j.matpur.2016.02.010
Publication status	Published - 1 Aug 2016

Access to Document

10.1016/j.matpur.2016.02.010

Cite this

@article{69207f635b0a4dfeb8b54c838bfe8c12,

title = "Stability results on the smoothness of optimal transport maps with general costs",

abstract = "We prove some stability results concerning the smoothness of optimal transport maps with general cost functions. In particular, we show that the smoothness of optimal transport maps is an open condition with respect to the cost function and the densities. As a consequence, we obtain regularity for a large class of transport problems, where the cost does not necessarily satisfy the MTW condition.",

keywords = "General costs, Optimal transportation, Regularity, Stability",

author = "Shibing Chen and Alessio Figalli",

note = "Publisher Copyright: {\textcopyright} 2016",

year = "2016",

month = aug,

day = "1",

doi = "10.1016/j.matpur.2016.02.010",

language = "English",

volume = "106",

pages = "280--295",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

number = "2",

}

TY - JOUR

T1 - Stability results on the smoothness of optimal transport maps with general costs

AU - Chen, Shibing

AU - Figalli, Alessio

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We prove some stability results concerning the smoothness of optimal transport maps with general cost functions. In particular, we show that the smoothness of optimal transport maps is an open condition with respect to the cost function and the densities. As a consequence, we obtain regularity for a large class of transport problems, where the cost does not necessarily satisfy the MTW condition.

AB - We prove some stability results concerning the smoothness of optimal transport maps with general cost functions. In particular, we show that the smoothness of optimal transport maps is an open condition with respect to the cost function and the densities. As a consequence, we obtain regularity for a large class of transport problems, where the cost does not necessarily satisfy the MTW condition.

KW - General costs

KW - Optimal transportation

KW - Regularity

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84963800195&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2016.02.010

DO - 10.1016/j.matpur.2016.02.010

M3 - Article

SN - 0021-7824

VL - 106

SP - 280

EP - 295

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 2

ER -

Stability results on the smoothness of optimal transport maps with general costs

Abstract

Access to Document

Other files and links

Fingerprint

Cite this