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dc.contributor.authorBenamou, Jean-David
dc.contributor.authorCarlier, Guillaume
dc.contributor.authorMérigot, Quentin
HAL ID: 235
dc.contributor.authorOudet, Edouard
dc.date.accessioned2014-08-27T09:35:55Z
dc.date.available2014-08-27T09:35:55Z
dc.date.issued2016
dc.identifier.issn0029-599X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13845
dc.language.isoenen
dc.subjectMonge–Ampère equation
dc.subject.ddc515en
dc.titleDiscretization of functionals involving the Monge-Ampère operator
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire Jean Kuntzmann (LJK) http://ljk.imag.fr CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology;France
dc.description.abstractenGradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The numerical applications of this formulation have been limited by the difficulty to compute the Wasserstein distance in dimension >= 2. One step of the JKO scheme is equivalent to a variational problem on the space of convex functions, which involves the Monge-Ampère operator. Convexity constraints are notably difficult to handle numerically, but in our setting the internal energy plays the role of a barrier for these constraints. This enables us to introduce a consistent discretization, which inherits convexity properties of the continuous variational problem. We show the effectiveness of our approach on nonlinear diffusion and crowd-motion models.
dc.relation.isversionofjnlnameNumerische Mathematik
dc.relation.isversionofjnlvol134
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages611-636
dc.relation.isversionofdoi10.1007/s00211-015-0781-y
dc.identifier.urlsitehttps://arxiv.org/abs/1408.4536v1
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
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dc.description.halcandidateoui
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T08:15:13Z


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