The edge algebra structure of the Zaremba problem

  • We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.

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Author:Der-Chen Chang, Nadia Habal, Bert-Wolfgang SchulzeGND
ISSN:1662-9981 (print)
ISSN:1662-999X (online)
Parent Title (English):Journal of pseudo-differential operators and applications
Place of publication:Basel
Document Type:Article
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
First Page:69
Last Page:155
Funder:NSF [DMS-1203845]; Hong Kong RGC Competitive Earmarked Research Grant at University of Macau [601410, MYRG115(Y1-L4)-FST13-QT]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert