Asymptotics of potentials in the edge calculus
Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptoti...
| Main Authors: | , |
|---|---|
| Format: | Others |
| Language: | English |
| Published: |
Universität Potsdam
2003
|
| Subjects: | |
| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26530 http://opus.kobv.de/ubp/volltexte/2008/2653/ |
| Summary: | Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics. |
|---|