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Boundary ε-regularity in optimal transportation

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dc.contributor.authorChen, Shibing
dc.contributor.authorFigalli, Alessio
dc.date.accessioned2015-06-01T03:09:33Z
dc.date.available2015-06-01T03:09:33Z
dc.date.issued2015
dc.date.updated2016-02-24T08:07:05Z
dc.description.abstractWe 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.
dc.description.sponsorshipThe second author has been partially supported by NSF Grant DMS-1262411. This material is based upon work supported by the National Science Foundation under Grant No. 0932078 000.en_AU
dc.format28 pages
dc.identifier.issn0001-8708en_AU
dc.identifier.urihttp://hdl.handle.net/1885/13661
dc.publisherElsevier
dc.rights© 2015 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ http://www.sherpa.ac.uk/romeo/issn/0001-8708/ Author can archive post-print (ie final draft post-refereeing) after 24 months embargo (Sherpa/Romeo 30/7/2017)
dc.sourceAdvances in Mathematics
dc.subjectOptimal transportation
dc.subjectMonge–Ampère
dc.subjectBoundary regularity
dc.subjectGeneral cost
dc.titleBoundary ε-regularity in optimal transportation
dc.typeJournal article
dcterms.dateAccepted2014-12-16
local.bibliographicCitation.lastpage567en_AU
local.bibliographicCitation.startpage540en_AU
local.contributor.affiliationChen, Shibing, Centre for Mathematics and Its Applications, CPMS Mathematical Sciences Institute, The Australian National Universityen_AU
local.contributor.authoruidu5623741en_AU
local.identifier.absfor010101 - Algebra and Number Theory
local.identifier.absfor010110 - Partial Differential Equations
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationa383154xPUB3013
local.identifier.citationvolume273en_AU
local.identifier.doi10.1016/j.aim.2014.12.032en_AU
local.identifier.essn1090-2082en_AU
local.identifier.scopusID2-s2.0-84921472124
local.publisher.urlhttp://www.elsevier.com/en_AU
local.type.statusAccepted Versionen_AU

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