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A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation
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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