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Corner Boundary Value Problems

  • Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.

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Metadaten
Author details:Der-Chen ChangGND, Tao Qian, Bert-Wolfgang SchulzeGND
DOI:https://doi.org/10.1007/s11785-014-0424-9
ISSN:1661-8254
ISSN:1661-8262
Title of parent work (English):Complex analysis and operator theory
Publisher:Springer
Place of publishing:Basel
Publication type:Article
Language:English
Year of first publication:2015
Publication year:2015
Release date:2017/03/27
Tag:Corner pseudo-differential operators; Ellipticity of corner-degenerate operators; Meromorphic operator-valued symbols
Volume:9
Issue:5
Number of pages:54
First page:1157
Last Page:1210
Funding institution:NSF [DMS-1203845]; University of Macau [MYRG115(Y1-L4)-FST13-QT]; Hong Kong RGC competitive earmarked research grant [601410]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:Referiert
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