Interior regularity of optimal transport paths

被引：47

作者：

Xia, QL ^{[1
]}

机构：

[1] Univ Texas, Dept Math, Austin, TX 78712 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2004年 / 20卷 / 03期

关键词：

Probability Measure; Line Segment; Present Article; Interior Point; Regularity Property;

D O I：

10.1007/s00526-003-0237-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：283 / 299

页数：17

共 13 条

[1] STRUCTURE OF STATIONARY ONE DIMENSIONAL VARIFOLDS WITH POSITIVE DENSITY [J].