论文标题
蒙加的解决方案和多核心最佳运输中的独特性：成本上的条件较弱，边际条件较强
Monge solutions and uniqueness in multi-marginal optimal transport: weaker conditions on the cost, stronger conditions on the marginals
论文作者
论文摘要
在假设给定的边际收集相对于局部坐标绝对是连续的，我们就在多 - 边界最佳运输问题中获得独特性和Monge解决方案建立了一般条件。当假定只有第一个边缘是绝对连续的时，我们的条件等同于[23]中发现的分裂集条件的扭曲。此外，当我们较早的工作中的特殊成本功能[32，33]中得到了满足，当时绝对连续性施加在某些其他边际集合中。我们还提出了几个新的成本功能示例，这些示例违反了分裂集条件的扭曲，但满足了此处介绍的新条件。因此，在适当的边际子集的规律性条件下，我们获得了这些成本函数的Monge解决方案和唯一性结果。
We establish a general condition on the cost function to obtain uniqueness and Monge solutions in the multi-marginal optimal transport problem, under the assumption that a given collection of the marginals are absolutely continuous with respect to local coordinates. When only the first marginal is assumed to be absolutely continuous, our condition is equivalent to the twist on splitting sets condition found in [23]. In addition, it is satisfied by the special cost functions in our earlier work [32, 33], when absolute continuity is imposed on certain other collections of marginals. We also present several new examples of cost functions which violate the twist on splitting sets condition but satisfy the new condition introduced here; we therefore obtain Monge solution and uniqueness results for these cost functions, under regularity conditions on an appropriate subset of the marginals.
