Geodesics for a class of distances in the space of probability measures

Nazaret, Bruno; Carlier, Guillaume; Cardaliaguet, Pierre

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

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00686908

Date

2013

Journal name

Calculus of Variations and Partial Differential Equations

Volume

Number

3-4

Publisher

Springer

Pages

395-420

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 / Keywords

optimality conditions; geodesics in the space of probability measures; power mobility; dynamical transport distances