The monge-ampère equation and its link to optimal transportation

Guido De Philippis; Alessio Figalli

doi:10.1090/S0273-0979-2014-01459-4

The monge-ampère equation and its link to optimal transportation

Guido De Philippis, Alessio Figalli

Mathematics

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

Abstract

We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.

Original language	English (US)
Pages (from-to)	527-580
Number of pages	54
Journal	Bulletin of the American Mathematical Society
Volume	51
Issue number	4
DOIs	https://doi.org/10.1090/S0273-0979-2014-01459-4
State	Published - 2014

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0273-0979-2014-01459-4

Cite this

@article{ecd21346e8e74457a87f860305dae6be,

title = "The monge-amp{\`e}re equation and its link to optimal transportation",

abstract = "We survey old and new regularity theory for the Monge-Amp{\`e}re equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Amp{\`e}re type equations arising in that context.",

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

year = "2014",

doi = "10.1090/S0273-0979-2014-01459-4",

language = "English (US)",

volume = "51",

pages = "527--580",

journal = "Bulletin of the American Mathematical Society",

issn = "0273-0979",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - The monge-ampère equation and its link to optimal transportation

AU - De Philippis, Guido

AU - Figalli, Alessio

PY - 2014

Y1 - 2014

N2 - We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.

AB - We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.

UR - http://www.scopus.com/inward/record.url?scp=84904913690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904913690&partnerID=8YFLogxK

U2 - 10.1090/S0273-0979-2014-01459-4

DO - 10.1090/S0273-0979-2014-01459-4

M3 - Article

AN - SCOPUS:84904913690

VL - 51

SP - 527

EP - 580

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

SN - 0273-0979

IS - 4

ER -

The monge-ampère equation and its link to optimal transportation

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this