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dc.contributor.authorGonzález Nogueras, María del Mar
dc.contributor.authorCaffarelli, Luis
dc.contributor.authorNguyen, Truyen
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2012-02-06T12:07:40Z
dc.date.available2012-02-06T12:07:40Z
dc.date.created2011-11
dc.date.issued2011-11
dc.identifier.citationGonzález, M.; Caffarelli, L.; Nguyen, Truyen. "A perturbation argument for a Monge-Ampere type equation arising in optimal transportation". 2011.
dc.identifier.urihttp://hdl.handle.net/2117/14957
dc.description.abstractWe prove some asymptotic interior regularity results for potential functions of optimal transportation problems with power costs. We show that our problems are equivalent to optimal transportation problems whose cost functions are sufficiently small perturbations of the quadratic cost but they do not satisfy the well known condition (A.3) guaranteeing regularity. The proof consists in a perturbation argument from the standard Monge- Amp`ere equation in order to obtain interior H¨older estimates for second derivatives of potentials, and a careful understanding of why we might fail to have an Alexandroff weak solution when restricted to subdomains. In particular, we provide some quantitative estimates along the way on how the equation degenerates near the boundary.
dc.format.extent57 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201113CafGN]
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshMonge-Ampère equation
dc.titleA perturbation argument for a Monge-Ampere type equation arising in optimal transportation
dc.typeExternal research report
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttp://www.ma1.upc.edu/recerca/preprints/2011/prepr201103gonzalez.pdf
dc.rights.accessOpen Access
local.identifier.drac8947644
dc.description.versionPreprint
local.citation.authorGonzález, M.; Caffarelli, L.; Nguyen, Truyen
local.citation.publicationNameA perturbation argument for a Monge-Ampere type equation arising in optimal transportation


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