Gemischte Randanfangswertaufgaben für hyperbolische Differentialoperatoren auf Räumen mit Kanten

在这个项目中，我们将研究边缘附近的双曲微分算子。更确切地说，我们将研究这类算子的初边值问题。事实上，这些问题应该被称为“初始-边界-边缘”值问题，因为我们还将规定沿边缘的条件。我们将在时空中的Soblev空间的适应尺度上建立适定性，其中这些空间包含由所考虑的微分算子所预测的靠近边缘的附加渐近信息。沿边缘的规定条件与这些渐近性密切相关。其中，假定沿边界满足一致Lopatinski条件，以得到关于解的更强的可能估计。在下一步，这些能量估计将被微局部化，以获得解的奇性的传播结果。此外，还将构建一个参数线。

In this project we shall study hyperbolic differential operators near edges. More precisely we will investigate initial-boundary value problems for such operators. In fact these problems should be termed "initial-boundary-edge" value problems, since we are going to prescribe also conditions along the edges. We will establish well-posedness in an adapted scale of Sobolev spaces in space-time, where these spaces incorporate additional asymptotic information near the edges as is predicted by the differential operator under consideration. The prescribed conditions along the edges are closely related to these asymptotics. Among others, an analogue of the uniform Lopatinski condition is assumed to be fulfilled along the edges to get the stronges possible estimates on the solution. In a next step these energy estimates will be microlocalized to achieve the propagation results for the singularities of the solutions. Furthermore, a parametrix will be constructed.