Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum

Perfekt, 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 doi: 10.1016/j.matpur.2020.07.001

Abstract/Summary

We 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/90343
Identification Number/DOI	10.1016/j.matpur.2020.07.001
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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