标题： 低正则性时空的格林算子 显示英文标题

标题： Green operators for low regularity spacetimes

摘要： 在本文中，我们为低正则性时空上的波动算子定义并构造了先进的和迟滞的格林算子。 为了做到这一点，我们要求时空满足广义双曲性条件，这等价于经典非齐次问题在零初始数据下的适定性，其中弱解具有适当的支撑。 此外，我们提供了一个显式公式，用于表示格林算子的核，该公式基于H 1的任意特征基和一个适合的格林矩阵，该矩阵解一个二阶常微分方程组。 显示英文摘要

摘要： In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well- posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs.