dc.contributor.author Caffarelli, Luis dc.contributor.author González Nogueras, María del Mar dc.contributor.author Nguyen, Truyen dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2014-03-26T07:03:34Z dc.date.created 2014-05-01 dc.date.issued 2014-05-01 dc.identifier.citation Caffarelli, 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.identifier.issn 0003-9527 dc.identifier.uri http://hdl.handle.net/2117/22385 dc.description.abstract We 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.extent 56 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials dc.subject.lcsh Differential equations, Partial dc.title A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation dc.type Article dc.subject.lemac Equacions diferencials parcials dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions dc.identifier.doi 10.1007/s00205-013-0709-6 dc.relation.publisherversion http://link.springer.com/content/pdf/10.1007%2Fs00205-013-0709-6.pdf dc.rights.access Restricted access - publisher's policy local.identifier.drac 13641219 dc.description.version Postprint (published version) dc.date.lift 10000-01-01 local.citation.author Caffarelli, L.; Gonzalez, M.; Nguyen, Truyen local.citation.publicationName Archive for rational mechanics and analysis local.citation.volume 212 local.citation.number 2 local.citation.startingPage 359 local.citation.endingPage 414
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