论文标题
最佳运输中的奇异设置的规律性
Regularity of singular set in optimal transportation
论文作者
论文摘要
在本文中，当目标由两个不相交凸域组成时，我们为最佳传输问题建立了规律性理论。这是出现奇异性的重要模型。即使奇异集没有表现出任何形式的凸度，我们还是通过开发新的方法来证明其更高阶的规律性，这些方法也具有许多其他应用。值得注意的是，我们的结果是在不需要源域的任何凸度的情况下实现的。这符合咖啡雷利的著名规律性理论。
In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not exhibit any form of convexity a priori, we prove its higher order regularity by developing novel methods, which also have many other applications. Notably, our results are achieved without requiring any convexity of the source domain. This aligns with Caffarelli's celebrated regularity theory.
