Gemischte Randanfangswertaufgaben für hyperbolische Differentialoperatoren auf Räumen mit Kanten

• Applicant: Professor Dr. Ingo Witt
• Subject Area: Mathematics
• Term: from 2004 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5423505

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.

• DFG Programme: Research Fellowships
• International Connection: United Kingdom
• Cooperation Partner: Professor Dr. Michael Ruzhansky