论文标题
最佳运输图的规律性变化方法：一般成本功能
Variational approach to regularity of optimal transport maps: general cost functions
论文作者
论文摘要
我们将各种方法扩展到规律性，以获取由高盛（Goldman）发起的最佳运输图和一般成本功能案例的第一作者。我们的主要结果是$ε$ - 限制性结果是Hölder连续密度之间的最佳传输图比De Philippis-Figalli结果略高的量化。新的贡献之一是使用几乎最小的贡献：如果成本在定量上接近欧几里得成本功能，那么对于一般成本的最佳运输问题的最小化是一种几乎是二次成本的少量型。这进一步凸显了我们的变异方法与De Giorgi的策略之间的联系，以$ε$ - 最小表面的限制性。
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $ε$-regularity result for optimal transport maps between Hölder continuous densities slightly more quantitative than the result by De Philippis-Figalli. One of the new contributions is the use of almost-minimality: if the cost is quantitatively close to the Euclidean cost function, a minimizer for the optimal transport problem with general cost is an almost-minimizer for the one with quadratic cost. This further highlights the connection between our variational approach and De Giorgi's strategy for $ε$-regularity of minimal surfaces.
