Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 34, Issue 4, Pages 991-1011Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.anihpc.2016.07.004
Keywords
Neumann-Poincare operator; Lipschitz domain; Spectrum; RCIP method; Resonance
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Funding
- A3 Foresight Program of Korea through NRF [NRF-2014K2A2A6000567]
- Korean Ministry of Science, ICT and Future Planning through NRF [NRF-2013R1A1A3012931]
- Swedish Research Council [621-2014-5159]
- National Research Foundation of Korea [2016R1A2B4011304, 2013R1A1A3012931, 21A20131412859] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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.
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