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A priori estimates and existence of solutions to the prescribed centroaffine curvature problem

Jian, Huaiyu; Lu, Jian; Wang, Xu-Jia

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In this paper we study the prescribed centroaffine curvature problem in the Euclidean space Rⁿ⁺¹. This problem is equivalent to solving a Monge–Ampère equation on the unit sphere. It corresponds to the critical case of the Blaschke–Santaló inequality. By approximation from the subcritical case, and using an obstruction condition and a blow-up analysis, we obtain sufficient conditions for the a priori estimates, and the existence of solutions up to a Lagrange multiplier.

dc.contributor.authorJian, Huaiyu
dc.contributor.authorLu, Jian
dc.contributor.authorWang, Xu-Jia
dc.date.accessioned2018-01-09T00:05:58Z
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/1885/139100
dc.description.abstractIn this paper we study the prescribed centroaffine curvature problem in the Euclidean space Rⁿ⁺¹. This problem is equivalent to solving a Monge–Ampère equation on the unit sphere. It corresponds to the critical case of the Blaschke–Santaló inequality. By approximation from the subcritical case, and using an obstruction condition and a blow-up analysis, we obtain sufficient conditions for the a priori estimates, and the existence of solutions up to a Lagrange multiplier.
dc.format.mimetypeapplication/pdf
dc.publisherElsevier
dc.rights© 2017 Elsevier B.V.
dc.sourceJournal of Functional Analysis
dc.titleA priori estimates and existence of solutions to the prescribed centroaffine curvature problem
dc.typeJournal article
local.identifier.citationvolume274
dc.date.issued2018
local.publisher.urlhttps://www.elsevier.com/
local.type.statusAccepted Version
local.contributor.affiliationJian, Huaiyu, Centre for Mathematics and Its Applications, The Australian National University
local.contributor.affiliationLu, Jian, Centre for Mathematics and Its Applications, The Australian National University
local.contributor.affiliationWang, Xu-Jia, Centre for Mathematics and Its Applications, The Australian National University
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage826
local.bibliographicCitation.lastpage862
local.identifier.doi10.1016/j.jfa.2017.08.024
dcterms.accessRightsOpen Access
dc.provenancehttp://www.sherpa.ac.uk/romeo/issn/0022-1236/..."Author's post-print on open access repository after an embargo period of between 12 months and 48 months" from SHERPA/RoMEO site (as at 8/01/18).
CollectionsANU Research Publications

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