Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem
Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem
复制标题
Monge-Kantorovich 问题的最优交通网络作为自由狄利克雷区域
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
E. Stepanov
中科院分区：
文献类型：
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作者：
G. Buttazzo;E. Stepanov
本文研究了给定人口密度和工作场所密度的城市中最优交通网络的构建问题。该网络由一个指定长度的封闭连接集来建模，其最优性条件是最小化表示总运输成本的Monge-Kantorovich函数。假设在两点之间运输单位质量的成本在网络外进行时与两点之间的距离成正比，在沿网络进行时可以忽略不计。同样的问题也可以看作是找到一个最优的Dirichlet区域，使传递给定两个度量的Monge-Kantorovich代价最小化。本文主要研究最优网络的定性拓扑和几何性质。给出了最优网络的一个温和的正则性结果。
In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation is carried out outside of the network, and negligible when it is carried out along the network. The same problem can be also viewed as finding an optimal Dirichlet zone minimizing the Monge-Kantorovich cost of transporting the given two measures. The paper basically studies qualitative topological and geometrical properties of optimal networks. A mild regularity result for optimal networks is also provided.