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

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Abstract

In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savaré. We first prove the existence of a potential function and then give necessary and sufficient 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.

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Authors and Affiliations

  1. Ceremade, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cedex 16, France

    P. Cardaliaguet, G. Carlier & B. Nazaret

Authors
  1. P. Cardaliaguet
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  2. G. Carlier
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  3. B. Nazaret
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Correspondence to P. Cardaliaguet.

Additional information

Communicated by L.Ambrosio.

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Cardaliaguet, P., Carlier, G. & Nazaret, B. Geodesics for a class of distances in the space of probability measures. Calc. Var. 48, 395–420 (2013). https://doi.org/10.1007/s00526-012-0555-7

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  • DOI: https://doi.org/10.1007/s00526-012-0555-7

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