An equivalent path functional formulation of branched transportation problems
An equivalent path functional formulation of branched transportation problems
复制标题
分支运输问题的等效路径函数表述
DOI：
10.3934/dcds.2011.29.845
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发表时间：
2010
影响因子：
1.1
通讯作者：
F. Santambrogio
中科院分区：
文献类型：
--
作者：
L. Brasco;F. Santambrogio
我们考虑了两个分支传输模型：Bernot等人介绍的模型。(Publ Mat 49：417-451,2005)，它利用
定义在Lipschitz路空间上的测度上的泛函，以及路
Brancolini等人提出的功能模型。(J EUR Math Soc 8：415-434,2006)，其中最小化定义的某些适当的动作泛函
在测量值Lipschitz曲线的空间上，得到了概率空间上的黎曼度量，支持原子测量，代价取决于每个原子的质量。
我们证明了根据Brasco(Ann Mat Pura Appl 189：95-125,2010)对后一个模型进行修改，则两个模型是等价的。
We consider two models for branched transport: the one introduced in Bernot et al. (Publ Mat 49:417-451, 2005), which makes use of
a functional defined on measures over the space of Lipschitz paths, and the path
functional model presented in Brancolini et al. (J Eur Math Soc 8:415-434, 2006), where one minimizes some suitable action functional defined
over the space of measure-valued Lipschitz curves, getting sort of a Riemannian metric on the space of probabilities, favouring atomic measures, with a cost depending on the masses of each of their atoms.
We prove that modifying the latter model according to Brasco (Ann Mat Pura Appl 189:95-125, 2010), then the two models turn out to be equivalent.