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On the local theory of prescribed Jacobian equations

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Trudinger, Neil

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We develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.

dc.contributor.authorTrudinger, Neil
dc.date.accessioned2014-05-30T05:56:04Z
dc.date.available2014-05-30T05:56:04Z
dc.identifier.issn10780947
dc.identifier.urihttp://hdl.handle.net/1885/11736
dc.description.abstractWe develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.
dc.format19 pages
dc.publisherAmerican Institute of Mathematical Sciences
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/1078-0947/ "...author can archive pre-print (ie pre-refereeing), v and publisher's version/PDF(online version).." from SHERPA/RoMEO site (as at 30/05/14)
dc.sourceDiscrete and Continuous Dynamical Systems - Series A 34.4 (2014): 1663-1681
dc.subjectConvexity
dc.subjectduality
dc.subjectexistence and regularity
dc.subjectgenerating function
dc.subjectprescribed Jacobian equations
dc.titleOn the local theory of prescribed Jacobian equations
dc.typeJournal article
local.identifier.citationvolume34
dc.date.issued2014-04
local.identifier.absfor010109 - Ordinary Differential Equations, Difference Equations and Dynamical Systems
local.identifier.ariespublicationU3488905xPUB1798
local.publisher.urlhttp://aimsciences.org/
local.type.statusPublished Version
local.contributor.affiliationTrudinger, Neil, ANU Centre for Mathematics and its Applications
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage1663
local.bibliographicCitation.lastpage1681
local.identifier.doi10.3934/dcds.2014.34.1663
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-10T11:15:07Z
local.identifier.scopusID2-s2.0-84886492837
local.identifier.thomsonID000325653000020
CollectionsANU Research Publications

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