Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum
Peer reviewed, Journal article
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Date
2021Metadata
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Original version
Journal des Mathématiques Pures et Appliquées. 2021, 145 130-162. 10.1016/j.matpur.2020.07.001Abstract
We consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann–Poincaré 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.