基于对偶的惩罚平均场对策的时间全局正则性
Global-in-time regularity via duality for congestion-penalized Mean Field Games
摘要：
在简单介绍了平均场游戏中最典型的问题之一，拥塞的情况下（代理支付的费用取决于他们访问的区域的密度），并在其变分结构，我们考虑的问题的规则性的最优解。一个对偶论证，在Y. Brenier对不可压缩流体力学，最近应用到MFG密度约束，可以很容易地得到一些索伯列夫规律性，局部的空间和时间。在本文中，我们证明，仔细分析的行为接近最后的时间允许扩展相同的结果，包括t = T。
英文摘要：
After a brief introduction to one of the most typical problems in Mean Field Games, the congestion case (where agents pay a cost depending on the density of the regions they visit), and to its variational structure, we consider the question of the regularity of the optimal solutions. A duality argument, used for the first time in a paper by Y. Brenier on incompressible fluid mechanics, and recently applied to MFG with density constraints, allows to easily get some Sobolev regularity, locally in space and time. In the paper we prove that a careful analysis of the behaviour close to the final time allows to extend the same result including t = T .
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
