Gemischte Randanfangswertaufgaben für hyperbolische Differentialoperatoren auf Räumen mit Kanten

在这个项目中，我们将研究靠近边的双曲微分算子。更确切地说，我们将研究这些算子的初边值问题。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Sobolev空间的自适应尺度中建立适定性，其中这些空间在边缘附近包含由所考虑的微分算子预测的附加渐近信息。沿边的规定条件与这些渐近性密切相关。其中，假设沿边缘满足一致Lopatinski条件的模拟，以获得对解的强可能估计。在下一步中，这些能量估计将被微定位，以获得解的奇点的传播结果。然后，构造一个参数矩阵。

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.