Partial regularity for optimal transport maps

Guido De Philippis; Alessio Figalli

doi:10.1007/s10240-014-0064-7

Partial regularity for optimal transport maps

Guido De Philippis, Alessio Figalli

Mathematics

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

Abstract

We prove that, for general cost functions on Rⁿ, or for the cost d²/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

Original language	English (US)
Pages (from-to)	81-112
Number of pages	32
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	121
Issue number	1
DOIs	https://doi.org/10.1007/s10240-014-0064-7
State	Published - Jun 27 2015

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s10240-014-0064-7

Cite this

@article{831da7de59304216bd8969a19d0cd349,

title = "Partial regularity for optimal transport maps",

abstract = "We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.",

author = "{De Philippis}, Guido and Alessio Figalli",

note = "Publisher Copyright: {\textcopyright} 2014, IHES and Springer-Verlag Berlin Heidelberg.",

year = "2015",

month = jun,

day = "27",

doi = "10.1007/s10240-014-0064-7",

language = "English (US)",

volume = "121",

pages = "81--112",

journal = "Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques",

issn = "0073-8301",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - Partial regularity for optimal transport maps

AU - De Philippis, Guido

AU - Figalli, Alessio

PY - 2015/6/27

Y1 - 2015/6/27

N2 - We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

AB - We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

UR - http://www.scopus.com/inward/record.url?scp=84929946309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929946309&partnerID=8YFLogxK

U2 - 10.1007/s10240-014-0064-7

DO - 10.1007/s10240-014-0064-7

M3 - Article

AN - SCOPUS:84929946309

SN - 0073-8301

VL - 121

SP - 81

EP - 112

JO - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

JF - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

IS - 1

ER -

Partial regularity for optimal transport maps

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this