有界区间上凹迁移率函数诱导的一类修正Wasserstein距离
On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals
摘要：
我们研究了一类新的氡措施之间的距离类似的研究在最近的论文Dolbeault，Nazaret萨瓦雷[DNS]。这些距离（更正确的伪距离，因为可以假设值$+\infty$）的定义概括的动态公式的Wasserstein距离的凹迁移率函数的装置。我们主要感兴趣的物理有趣的情况下（不考虑在[DNS]）的凹流动性函数定义在一个有界区间。我们的状态的基本性质的措施赋予这个伪距离的空间。最后，我们详细研究了两种情况：定义在有限矩的$R^d$中的测度集和定义在有界凸集中的测度集。在这两种情况下，我们给出了序列关于距离收敛的充分条件，并证明了序列的有界性。
英文摘要：
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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