论文标题
尖锐的边界$ \ varepsilon $ - 最佳传输地图的频率
Sharp boundary $\varepsilon$-regularity of optimal transport maps
论文作者
论文摘要
在本文中，我们开发了一个边界$ \ varepsilon $ -Regularity理论，用于使用$ c^{1，α} $ - 边界之间的有限开放集之间的最佳传输图。我们的主要结果断言尖锐的$ c^{1，α} $ - 在某些假设下以线性估算的形式在边界处的运输图的规律性：主要的定量假设是，局部的非量化运输成本很小，边界在$ c^{1，α} $中几乎是本地平坦的。我们的方法是完全变化的，并建立在最近开发的内部规律性理论的基础上。
In this paper we develop a boundary $\varepsilon$-regularity theory for optimal transport maps between bounded open sets with $C^{1,α}$-boundary. Our main result asserts sharp $C^{1,α}$-regularity of transport maps at the boundary in form of a linear estimate under certain assumptions: The main quantitative assumptions are that the local nondimensionalized transport cost is small and that the boundaries are locally almost flat in $C^{1,α}$. Our method is completely variational and builds on the recently developed interior regularity theory.
