Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrumPerfekt, K.-M. (2021) Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum. Journal de Mathématiques Pures et Appliquées, 145. pp. 130-162. ISSN 0021-7824
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.matpur.2020.07.001 Abstract/SummaryWe consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann--Poincare operator of the boundary. A limiting absorption principle is proved, valid when the spectral parameter approaches the essential spectrum. Putting the principle into use, it is proved that the corner produces absolutely continuous spectrum of multiplicity 1. The embedded eigenvalues are discrete. In particular, there is no singular continuous spectrum.
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