TY  - JOUR
A1  - Dines, Nicoleta
A1  - Liu, Xiaochun
A1  - Schulze, Bert-Wolfgang
T1  - Edge quantisation of elliptic operators
T2  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
N2  - The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy sigma = (sigma(psi), sigma(boolean AND)), where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol sigma(boolean AND) which includes the (in general not explicity known) number of additional conditions of trace and potential type on the edge. We focus here on these questions 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.
Y1  - 2009
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/30761
UR  - http://www.springerlink.com/content/103082
SN  - 1437-739X
ER  -