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arXiv · 0909.2512

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

Stefano Lisini·Antonio Marigonda
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Abstract

We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savaré [DNS]. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined generalizing the dynamical formulation of the Wasserstein distance by means of a concave mobility function. We are mainly interested in the physical interesting case (not considered in [DNS]) of a concave mobility function defined in a bounded interval. We state the basic properties of the space of measures endowed with this pseudo-distance. Finally, we study in detail two cases: the set of measures defined in $R^d$ with finite moments and the set of measures defined in a bounded convex set. In the two cases we give sufficient conditions for the convergence of sequences with respect to the distance and we prove a property of boundedness.

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Stefano Lisini, Antonio Marigonda. 2009-09-14. On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals. https://arxiv.org/abs/0909.2512

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