
On the Wasserstein distance between mutually singular measures
Buttazzo, Giuseppe; Carlier, Guillaume; Laborde, Maxime (2018), On the Wasserstein distance between mutually singular measures, Advances in Calculus of Variations, 13, 2, p. 141–154. 10.1515/acv-2017-0036
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Type
Article accepté pour publication ou publiéDate
2018Nom de la revue
Advances in Calculus of VariationsVolume
13Numéro
2Éditeur
De Gruyter
Pages
141–154
Identifiant publication
Métadonnées
Afficher la notice complèteAuteur(s)
Buttazzo, GiuseppeDipartimento di Matematica [Pisa]
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laborde, Maxime
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
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.Mots-clés
Wasserstein distance; singular measures; perimeter penalizationPublications associées
Affichage des éléments liés par titre et auteur.
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Buttazzo, Giuseppe; Carlier, Guillaume; Eichinger, Katharina (2022) Document de travail / Working paper
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Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime (2016) Article accepté pour publication ou publié
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Buttazzo, Giuseppe; Carlier, Guillaume; Comte, Myriam (2007-03) Article accepté pour publication ou publié
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Buttazzo, Giuseppe; Carlier, Guillaume; Tahraoui, Rabah (2010) Article accepté pour publication ou publié
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Carlier, Guillaume; Chizat, Lenaic; Laborde, Maxime (2022) Document de travail / Working paper