TY  - INPR
A1  - Dines, Nicoleta
A1  - Liu, X.
A1  - Schulze, Bert-Wolfgang
T1  - Edge quantisation of elliptic operators
N2  - The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.
T3  - Preprint - (2004) 24 
KW  - Boundary value problems
KW  - edge singularities
KW  - ellipticity
KW  - spectral flow
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2482
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-26838
ER  -