Spectral Resolution of the Neumann–Poincaré Operator on Intersecting Disks and Analysis of Plasmon Resonance

Hyeonbae Kang; Mikyoung Lim; Sanghyeon Yu

doi:10.1007/s00205-017-1129-9

Spectral Resolution of the Neumann–Poincaré Operator on Intersecting Disks and Analysis of Plasmon Resonance

Hyeonbae Kang^*
, Mikyoung Lim
, Sanghyeon Yu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

The purpose of this paper is to investigate the spectral nature of the Neumann–Poincaré operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows, in particular, that it admits only the absolutely continuous spectrum; no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution of the plasmon resonance at the absolutely continuous spectrum.

Original language	English
Pages (from-to)	83-115
Number of pages	33
Journal	Archive for Rational Mechanics and Analysis
Volume	226
Issue number	1
DOIs	https://doi.org/10.1007/s00205-017-1129-9
Publication status	Published - 2017 Oct 1
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-017-1129-9

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abstract = "The purpose of this paper is to investigate the spectral nature of the Neumann–Poincar{\'e} operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows, in particular, that it admits only the absolutely continuous spectrum; no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution of the plasmon resonance at the absolutely continuous spectrum.",

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AB - The purpose of this paper is to investigate the spectral nature of the Neumann–Poincaré operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows, in particular, that it admits only the absolutely continuous spectrum; no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution of the plasmon resonance at the absolutely continuous spectrum.

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Spectral Resolution of the Neumann–Poincaré Operator on Intersecting Disks and Analysis of Plasmon Resonance

Abstract

Bibliographical note

ASJC Scopus subject areas

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