Advances in Differential Equations
- Adv. Differential Equations
- Volume 21, Number 11/12 (2016), 1117-1164.
A new optimal transport distance on the space of finite Radon measures
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.
Adv. Differential Equations Volume 21, Number 11/12 (2016), 1117-1164.
First available in Project Euclid: 13 October 2016
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Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ade/1476369298.