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Spectral analysis of Neumann-Poincare operators and its applications

Research Project

Project/Area Number 17K05303
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionEhime University

Principal Investigator

ANDO Kazunori  愛媛大学, 理工学研究科(工学系), 准教授 (70774884)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsスペクトル解析 / ノイマン-ポアンカレ作用素 / プラズモン共鳴 / スペクトル理論 / 散乱理論 / レゾナンス / 解析学 / 数理物理 / 応用数学
Outline of Final Research Achievements

We have studied the relationship between the eigenvalues of Neumann-Poincare operators which are boundary integral operators, and the smoothness of the boundary, mainly in two-dimansions. The decay rate of the eigenvalues of Neumann-Poincare operator has a close relationship with anomalous localized resonance. We have studied the Neumann-Poincare operator associated to both the Laplace operator and the Lame operator, and we obtained the followings: if the boundary is an analytic curve, then the eigenvalues of Neumann-Poincare operator accumulate exponentially.

Academic Significance and Societal Importance of the Research Achievements

異常局在共鳴とは、数学的には微分方程式の楕円性が崩れる際にある条件のもとに見られる現象で、領域外部にエネルギーの供給源がある場合に領域境界上でエネルギーの異常な高まりを示し、遠方では微分方程式の解が有界となることである。異常局在共鳴は、物理的にも大変興味深い現象でクローキングやスーパーレンズなど、さまざまな応用が考えられている。異常局在共鳴を示す際には、ノイマン-ポアンカレ作用素の固有値の集積の速さが密接に関係していることが知られており、今後の研究でどのような性質をもった領域で異常局在共鳴が起こるかを研究する際の足掛かりとなる研究である。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (13 results)

All 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (1 results) Journal Article (4 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results) Presentation (8 results) (of which Int'l Joint Research: 6 results,  Invited: 4 results)

  • [Int'l Joint Research] Inha University(韓国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Spectral analysis of Neumann-Poincare operator2021

    • Author(s)
      Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi, Mihai Putinar
    • Journal Title

      ROMANIAN JOURNAL OF PURE AND APPLIED MATHEMATICS

      Volume: -

    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] The First Hadamard Variation of Neumann-Poincare eigenvalues on the sphere2019

    • Author(s)
      Kazunori Ando, Yoshihisa Miyanishi, Hyeonbae Kang and Erika Ushikoshi
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 147 Issue: 3 Pages: 1073-1080

    • DOI

      10.1090/proc/14246

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Elastic Neumann-Poincare Operators on Three Dimensional Smooth Domains: Polynomial Compactness and Spectral Structure2019

    • Author(s)
      Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi
    • Journal Title

      INTERNATIONAL MATHEMATICS RESEARCH NOTICES

      Volume: 2019 Issue: 12 Pages: 3883-3900

    • DOI

      10.1093/imrn/rnx258

    • Related Report
      2019 Research-status Report 2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Exponential decay estimates of the eigenvalues for the Neumann-Poincare operator on analytic boundaries in two dimensions2018

    • Author(s)
      Kazunori Ando, Yoshihisa Miyanishi and Hyeonbae Kang
    • Journal Title

      Journal of Integral Equations and Applications

      Volume: 30 Issue: 4 Pages: 473-489

    • DOI

      10.1216/jie-2018-30-4-473

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Eigenvalues of the Neumann-Poincare operator in two dimensions2020

    • Author(s)
      安藤和典
    • Organizer
      微分方程式の総合的研究
    • Related Report
      2020 Annual Research Report
  • [Presentation] Spectral properties of the Neumann-Poincaré operators and anomalous localized resonance2020

    • Author(s)
      Kazunori Ando
    • Organizer
      スペクトル・散乱 那覇シンポジウム
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Eigenvalues of the Neumann-Poincaré operators in two dimensions2019

    • Author(s)
      Kazunori Ando
    • Organizer
      The 9th Congress of Romanian Mathematicians
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The eigenvalues of the elastic Neumann-Poincaré operator in two dimensions2019

    • Author(s)
      Kazunori Ando
    • Organizer
      Mini-workshop: Neumann-Poincaré operator and related topics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] The eigenvalues of the elastic Neumann-Poincare operator in two dimensions2019

    • Author(s)
      安藤和典
    • Organizer
      Mini-workshop: Neumann-Poincare operator and related topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Spectral analysis of the NP operator in two dimensions and cloaking by anomalous localized resonance2018

    • Author(s)
      Kazunori Ando
    • Organizer
      International Workshop: The Neumann-Poincare Operator, Plasmonics, and Field Concentration
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral analysis of the elastic Neumann-Poincare operator and cloaking by anomalous localized resonance2018

    • Author(s)
      Kazunori Ando
    • Organizer
      The 3rd East Asia Section of IPIA Young Scholars Symposium
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 弾性方程式に対するノイマン-ポアンカレ作用素のスペクトルについて2017

    • Author(s)
      安藤和典
    • Organizer
      夏の作用素論シンポジウム
    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2022-01-27  

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