Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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SPECTRAL PROPERTIES OF THE NEUMANN-POINCARÉ OPERATOR AND CLOAKING BY ANOMALOUS LOCALIZED RESONANCE: A REVIEW

  • SHOTA FUKUSHIMA (DEPARTMENT OF MATHEMATICS AND INSTITUTE OF APPLIED MATHEMATICS, INHA UNIVERSITY) ;
  • YONG-GWAN JI (SCHOOL OF MATHEMATICS, KOREA INSTITUTE FOR ADVANCED STUDY) ;
  • HYEONBAE KANG (DEPARTMENT OF MATHEMATICS AND INSTITUTE OF APPLIED MATHEMATICS, INHA UNIVERSITY) ;
  • YOSHIHISA MIYANISHI (DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, SHINSHU UNIVERSITY)
  • Received : 2023.05.08
  • Accepted : 2023.06.20
  • Published : 2023.06.25
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Abstract

This is a review paper on recent development on the spectral theory of the Neumann-Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the Neumann-Poincaré operator and surface localization of the single layer potentials of its eigenfunctions. Study on these topics is motivated by their relations with the cloaking by anomalous localized resonance. We review on this topic as well.

Keywords

Acknowledgement

This work is partially supported by National Research Foundation (of S. Korea) grants No. 2022R1A2B5B01001445 and by a KIAS Individual Grant (MG089001) at Korea Institute for Advanced Study.

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