On the Regularity of Optimal Transports Between Degenerate Densities
On the Regularity of Optimal Transports Between Degenerate Densities
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DOI：
10.1007/s00205-022-01796-y
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发表时间：
2021-05
影响因子：
2.5
通讯作者：
Yash Jhaveri;O. Savin
中科院分区：
文献类型：
--
作者：
Yash Jhaveri;O. Savin
通过证明退化密度之间最优运输的正则性结果，我们研究了二次费用最优运输问题的最常见的映象和非形式化描述，也被称为Monge-Ampère方程的第二边值问题--用给定的沙堆填充洞的最有效方法是什么？特别是，我们的工作包含了对孔洞和沙堆由集中在有界凸区域上的绝对连续测量表示的设置的分析，其密度表现为到这些区域边界的距离函数的非负幂。
We study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value problem for the Monge–Ampère equation—what is the most efficient way to fill a hole with a given pile of sand?—by proving regularity results for optimal transports between degenerate densities. In particular, our work contains an analysis of the setting in which holes and sandpiles are represented by absolutely continuous measures concentrated on bounded convex domains whose densities behave like nonnegative powers of the distance functions to the boundaries of these domains.