论文标题
在确定性解决方案上，用于多核心最佳运输，库仑成本
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
论文作者
论文摘要
在本文中，我们研究了飞机上的库仑成本$ \ r^2 $的三边界最佳质量运输问题。关键问题是最初由科伦坡和stra驳斥的所谓Seidl地图的最佳性。我们概括了科伦坡和Stra获得的部分阳性结果，并为径向库仑成本提供了必要和足够的条件，使其与更简单的成本相吻合，这与所有三个粒子对齐的情况相对应。此外，我们为这个地图家族的最佳性提供了无限的常规反例。
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite class of regular counterexamples to the optimality of this family of maps.
