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dc.contributor.authorCaffarelli, Luis
dc.contributor.authorGonzález Nogueras, María del Mar
dc.contributor.authorNguyen, Truyen
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.identifier.citationCaffarelli, L.; Gonzalez, M.; Nguyen, Truyen. A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation. "Archive for rational mechanics and analysis", 01 Maig 2014, vol. 212, núm. 2, p. 359-414.
dc.description.abstractWe prove some interior regularity results for potential functions of optimal transportation problems with power costs. The main point is that our problem is equivalent to a new optimal transportation problem whose cost function is a sufficiently small perturbation of the quadratic cost, but it does not satisfy the well known condition (A.3) guaranteeing regularity. The proof consists in a perturbation argument from the standard Monge–Ampère equation in order to obtain, first, interior C1,1 estimates for the potential and, second, interior Hölder estimates for second derivatives. In particular, we take a close look at the geometry of optimal transportation when the cost function is close to quadratic in order to understand how the equation degenerates near the boundary.
dc.format.extent56 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
dc.subject.lcshDifferential equations, Partial
dc.titleA Perturbation argument for a Monge–Ampère type equation arising in optimal transportation
dc.subject.lemacEquacions diferencials parcials
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
local.citation.authorCaffarelli, L.; Gonzalez, M.; Nguyen, Truyen
local.citation.publicationNameArchive for rational mechanics and analysis

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