Advances in Differential Equations

A new optimal transport distance on the space of finite Radon measures

Stanislav Kondratyev, Léonard Monsaingeon, and Dmitry Vorotnikov

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Abstract

We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula. We establish various topological and geometrical properties of the resulting metric space, derive some formal Riemannian structure, and develop differential calculus following F. Otto's approach. Finally, we apply these ideas to identify a model of animal dispersal proposed by MacCall and Cosner as a gradient flow in our formalism and obtain new long-time convergence results.

Article information

Source
Adv. Differential Equations Volume 21, Number 11/12 (2016), 1117-1164.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
http://projecteuclid.org/euclid.ade/1476369298

Mathematical Reviews number (MathSciNet)
MR3556762

Subjects
Primary: 28A33: Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 35Q92: PDEs in connection with biology and other natural sciences 49Q20: Variational problems in a geometric measure-theoretic setting 58B20: Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]

Citation

Kondratyev, Stanislav; Monsaingeon, Léonard; Vorotnikov, Dmitry. A new optimal transport distance on the space of finite Radon measures. Adv. Differential Equations 21 (2016), no. 11/12, 1117--1164. http://projecteuclid.org/euclid.ade/1476369298.


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