论文标题
通过通行费的最佳运输
Optimal transport through a toll
论文作者
论文摘要
我们通过沿路径的收缩来解决具有二次成本功能的最佳运输问题，并限制了通量的限制。收缩在概念上由收费站表示，限制了跨越流速。我们提供了一种精确的公式，此外，它可以在较高维度中的概括。我们通过证明存在和解决方案的独特性来详细研究在一个维度中运输的情况。在适当的规律性假设下，我们对运输计划进行明确的构造。讨论了对较高维度的通量约束的概括和理论的可能扩展。
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.
