Classification of spectra of the Neumann-Poincare operator on planar domains with corners by resonance

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We study spectral properties of the Neumann-Poincare operator on planar domains with corners with particular emphasis on existence of continuous spectrum and pure point spectrum. We show that the rate of resonance at continuous spectrum is different from that at eigenvalues, and then derive a method to distinguish continuous spectrum from eigenvalues. We perform computational experiments using the method to see whether continuous spectrum and pure point spectrum appear on domains with corners. For the computations we use a modification of the Nystrom method which makes it possible to construct high-order convergent discretizations of the Neumann-Poincare operator on domains with corners. The results of experiments show that all three possible spectra, absolutely continuous spectrum, singularly continuous spectrum, and pure point spectrum, may appear depending on domains. We also prove rigorously two properties of spectrum which are suggested by numerical experiments: symmetry of spectrum (including continuous spectrum), and existence of eigenvalues on rectangles of high aspect ratio. (C) 2016 Elsevier Masson SAS. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2017-07
Language
English
Article Type
Article
Keywords

CONDUCTIVITY

Citation

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, v.34, no.4, pp.991 - 1011

ISSN
0294-1449
DOI
10.1016/j.anihpc.2016.07.004
URI
http://hdl.handle.net/10203/225085
Appears in Collection
MA-Journal Papers(저널논문)
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