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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Author:Der-Chen Chang, Tao Qian, Bert-Wolfgang SchulzeGND
ISSN:1661-8254 (print)
ISSN:1661-8262 (online)
Parent Title (English):Complex analysis and operator theory
Place of publication:Basel
Document Type:Article
Year of first Publication:2015
Year of Completion:2015
Release Date:2017/03/27
Tag:Corner pseudo-differential operators; Ellipticity of corner-degenerate operators; Meromorphic operator-valued symbols
First Page:1157
Last Page:1210
Funder: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