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November/December 2016 A new optimal transport distance on the space of finite Radon measures
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
Adv. Differential Equations 21(11/12): 1117-1164 (November/December 2016).

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.

Citation

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Stanislav Kondratyev. Léonard Monsaingeon. Dmitry Vorotnikov. "A new optimal transport distance on the space of finite Radon measures." Adv. Differential Equations 21 (11/12) 1117 - 1164, November/December 2016.

Information

Published: November/December 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1375.49062
MathSciNet: MR3556762

Subjects:
Primary: 28A33, 35Q92, 49Q20, 58B20

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 11/12 • November/December 2016
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