hal.structure.identifier Dipartimento di Matematica [Pisa] dc.contributor.author Buttazzo, Giuseppe * hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Carlier, Guillaume * hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Laborde, Maxime * dc.date.accessioned 2017-11-06T10:13:13Z dc.date.available 2017-11-06T10:13:13Z dc.date.issued 2018 dc.identifier.issn 1864-8258 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/16916 dc.language.iso en en dc.subject Wasserstein distance dc.subject singular measures dc.subject perimeter penalization dc.subject.ddc 515 en dc.title On the Wasserstein distance between mutually singular measures dc.type Article accepté pour publication ou publié dc.description.abstracten We study the Wasserstein distance between two measures µ, ν which are mutually singular. In particular, we are interested in minimization problems of the form W (µ, A) = inf W (µ, ν) : ν ∈ A where µ is a given probability and A is contained in the class µ ⊥ of probabilities that are singular with respect to µ. Several cases for A are considered; in particular, when A consists of L 1 densities bounded by a constant, the optimal solution is given by the characteristic function of a domain. Some regularity properties of these optimal domains are also studied. Some numerical simulations are included, as well as the double minimization problem min P (B) + kW (A, B) : |A ∩ B| = 0, |A| = |B| = 1 , where k > 0 is a fixed constant, P (A) is the perimeter of A, and both sets A, B may vary. dc.relation.isversionofjnlname Advances in Calculus of Variations dc.relation.isversionofjnlvol 13 dc.relation.isversionofjnlissue 2 dc.relation.isversionofjnldate 2018 dc.relation.isversionofjnlpages 141–154 dc.relation.isversionofdoi 10.1515/acv-2017-0036 dc.relation.isversionofjnlpublisher De Gruyter dc.subject.ddclabel Analyse en dc.description.ssrncandidate non dc.description.halcandidate non dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2020-07-01T12:05:25Z hal.author.function aut hal.author.function aut hal.author.function aut
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