A new optimal transport distance on the space of finite Radon measures. (English) Zbl 1375.49062

Summary: 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.


49Q20 Variational problems in a geometric measure-theoretic setting
28A33 Spaces of measures, convergence of measures
35L60 First-order nonlinear hyperbolic equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
Full Text: arXiv Euclid