Spectral properties of the Neumann-Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system

Kazunori Ando, Yong Gwan Ji, Hyeonbae Kang, Kyoungsun Kim, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We first investigate spectral properties of the Neumann-Poincaré (NP) operator for the Lamé system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for the Laplace operator. We then show that even if elasto-static NP operator is not compact even on smooth domains, it is polynomially compact and its spectrum on two-dimensional smooth domains consists of eigenvalues that accumulate to two different points determined by the Lamé constants. We then derive explicitly eigenvalues and eigenfunctions on discs and ellipses. Using these resonances occurring at eigenvalues is considered. We also show on ellipses that cloaking by anomalous localized resonance takes place at accumulation points of eigenvalues.

Original languageEnglish
Pages (from-to)189-225
Number of pages37
JournalEuropean Journal of Applied Mathematics
Volume29
Issue number2
DOIs
Publication statusPublished - 2018 Apr 1
Externally publishedYes

Keywords

  • cloaking by anomalous localized resonance
  • Lamé system
  • linear elasticity
  • Neumann-Poincaré operator
  • resonance
  • spectrum

ASJC Scopus subject areas

  • Applied Mathematics

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