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Classification of s...
Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance
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- Helsing, Johan (författare)
- Lund University,Lunds universitet,Harmonic Analysis and Applications,Forskargrupper vid Lunds universitet,Lund University Research Groups
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- Kang, Hyeonbae (författare)
- Inha University
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- Lim, Mikyoung (författare)
- Korea Advanced Institute of Science and Technology (KAIST)
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(creator_code:org_t)
- European Mathematical Society - EMS - Publishing House GmbH, 2017
- 2017
- Engelska 21 s.
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Ingår i: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 34:4, s. 991-1011
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http://dx.doi.org/10...
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https://ems.press/co...
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https://lup.lub.lu.s...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We study spectral properties of the Neumann–Poincaré 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 Nyström method which makes it possible to construct high-order convergent discretizations of the Neumann–Poincaré 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Lipschitz domain
- Neumann–Poincaré operator
- RCIP method
- Resonance
- Spectrum
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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