Interior regularity of optimal transport paths
Interior regularity of optimal transport paths
复制标题
最佳运输路径的内部规律性
DOI：
10.1007/s00526-003-0237-6
复制
发表时间：
2004
影响因子：
2.1
通讯作者：
Qinglan Xia
中科院分区：
文献类型：
--
作者：
Qinglan Xia
在以前的论文[12]中，我们考虑了将一个概率测度运输到另一个概率测度的成本由运输路径而不是运输图给出的问题。在这种模式下，重叠运输往往更经济。在本文中，我们研究的内部正则性质的最佳运输路径。我们证明了有限成本的最优运输路径是可求长的，并且简单地说是路径的每个内点附近的线段的有限并集。
Abstract.In a previous paper [12], we considered problems for which the cost of transporting one probability measure to another is given by a transport path rather than a transport map. In this model overlapping transport is frequently more economical. In the present article we study the interior regularity properties of such optimal transport paths. We prove that an optimal transport path of finite cost is rectifiable and simply a finite union of line segments near each interior point of the path.