Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum
Spectral Theory
2020-10-13 v2 Functional Analysis
Abstract
We consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann--Poincar\'e 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.
Cite
@article{arxiv.1911.12294,
title = {Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum},
author = {Karl-Mikael Perfekt},
journal= {arXiv preprint arXiv:1911.12294},
year = {2020}
}
Comments
31 pages, 4 figures. To appear in Journal de Math\'ematiques Pures et Appliqu\'ees