We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo ‘lower order terms’) by a principal symbolic
hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and
σ ^(A)(y, η), (y, η) 2 T*Y 0, the (operator-valued) edge symbol of ‘first generation’, cf. [15]. The novelty here is the edge symbol σ^ of ‘second generation’, parametrised by (z, Ϛ) 2 T*Z 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind.
We show the continuity of corner-degenerate operators in weighted edge Sobolev
spaces, and we investigate the ellipticity of edge symbols of second generation.
Starting from parameter-dependent elliptic families of edge operators of first
generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:2975 |
| Date | January 2005 |
| Creators | Calvo, D., Schulze, Bert-Wolfgang |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Preprint |
| Format | application/pdf |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
Page generated in 0.0016 seconds