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.
Author details: | Der-Chen ChangGND, Tao Qian, Bert-Wolfgang SchulzeGND |
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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 |