Edge quantisation of elliptic operators

  • 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 edgeThe 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.show moreshow less

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Metadaten
Author:Nicoleta DinesGND, Xiaochun Liu, Bert-Wolfgang SchulzeGND
URL:http://www.springerlink.com/content/103082
DOI:https://doi.org/10.1007/s00605-008-0058-y
ISSN:1437-739X
Parent Title (English):Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Document Type:Article
Language:English
Year of first Publication:2009
Year of Completion:2009
Release Date:2017/03/25
Source:Monatshefte für Mathematik. - ISSN 0026-9255. - 156 (2009), 3, S. 233 - 274
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik und Computational Science
Peer Review:Nicht ermittelbar
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik