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dc.contributor.authorSavaré, Giuseppe
dc.contributor.authorNazaret, Bruno
HAL ID: 7130
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.subjectGradient flows
dc.subjectContinuity equation
dc.subjectKantorovich-Rubinstein-Wasserstein distance
dc.subjectOptimal transporten
dc.titleA new class of transport distances between measuresen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversita degli studi di Pavia;Italie
dc.description.abstractenWe introduce a new class of distances between nonnegative Radon measures on the euclidean space. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou and Brenier and provide a wide family interpolating between Wasserstein and homogeneous Sobolev distances. From the point of view of optimal transport theory, these distances minimize a dynamical cost to move a given initial distribution of mass to a final configuration. An important difference with the classical setting in mass transport theory is that the cost not only depends on the velocity of the moving particles but also on the densities of the intermediate configurations with respect to a given reference measure. We study the topological and geometric properties of these new distances, comparing them with the notion of weak convergence of measures and the well established Kantorovich-Rubinstein-Wasserstein theory. An example of possible applications to the geometric theory of gradient flows is also given.en
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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