Advances in Differential Equations

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

Stanislav Kondratyev, Léonard Monsaingeon, and Dmitry Vorotnikov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 13 October 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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.

Export citation