Geodesics for a class of distances in the space of probability measures
Nazaret, Bruno; Carlier, Guillaume; Cardaliaguet, Pierre (2013), Geodesics for a class of distances in the space of probability measures, Calculus of Variations and Partial Differential Equations, 48, 3-4, p. 395-420. http://dx.doi.org/10.1007/s00526-012-0555-7
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00686908
Journal nameCalculus of Variations and Partial Differential Equations
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Abstract (EN)In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the existence of a potential function and then give necessary and suffi cient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves.
Subjects / Keywordsoptimality conditions; geodesics in the space of probability measures; power mobility; dynamical transport distances
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