论文标题
Hölder定期生成的雅各布方程
Hölder regularity of solutions to generated Jacobian equations
论文作者
论文摘要
生成的雅各布方程是Monge-Ampère类型方程，其中包含最佳运输作为特殊情况。因此，最佳运输案例具有自己的特殊结构，对于更一般的雅各布方程来说，不一定是正确的。因此，无法将最佳运输的理论直接移植到产生的雅各布方程。在本文中，我们指出了阻止证明的困难，直接从\ cite {loeper2009ontr}到生成的雅各布方程的当地霍德定期解决了最佳运输问题的解决方案，然后我们讨论如何处理这些困难，并证明生成的雅各比式等方程中的本地Hölder规律性。
Generated Jacobian equations are Monge-Ampère type equations which contain optimal transport as a special case. Therefore, optimal transport case has its own special structure which is not necessarily true for more general generated Jacobian equations. Hence the theory for optimal transport can not be directly transplanted to generated Jacobian equations. In this paper, we point out the difficulties that prevent applying the proof the local Hölder regularity of solutions of optimal transport problem from \cite{Loeper2009OnTR} directly to Generated Jacobian Equations, we then discuss how to handle these difficulties, and prove local Hölder regularity in the generated Jacobian equation case.
