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Best evaluation of the Sobolev inequality using the reproducing kernel theory and its applications

Research Project

Project/Area Number 25400210
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionNihon University

Principal Investigator

TAKEMURA Kazuo  日本大学, 理工学部, 准教授 (60367216)

Co-Investigator(Kenkyū-buntansha) 亀高 惟倫  大阪大学, その他部局等, 名誉教授 (00047218)
楳田 登美男  兵庫県立大学, 物質理学研究科, 教授 (20160319)
Co-Investigator(Renkei-kenkyūsha) NAGAI Atsushi  日本大学, 生産工学部, 教授 (90304039)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsソボレフ不等式 / 最良定数 / グリーン行列 / 再生核 / グリーン関数
Outline of Final Research Achievements

The subject of this research is to obtain best evaluation of a Sobolev inequality. In continuous version, we have treated of Thomson cable (a continuous model) and a free boundary value problem for a 2M-th order operator (no lower terms). In discrete version, we have treated the Mobius ladder, C60 fullerene buckyball, the truncated regular M-hedron (M=4,6,8) and the Toeplitz graph. In each case, we have computed a best constant and family of best functions for the Sobolev inequality. These are important results to become the clue in studying the future Sobolev inequality.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (10 results)

All 2016 2015 2014 2013 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results,  Open Access: 3 results,  Acknowledgement Compliant: 4 results) Presentation (2 results)

  • [Journal Article] Two types of discrete Sobolev inequalities on a weighted Toeplitz graph2016

    • Author(s)
      Kazuo Takemura, Atsushi Nagai, Yoshinori Kametaka
    • Journal Title

      Linear Algebra and its Applicatoins

      Volume: 507 Pages: 344-355

    • DOI

      10.1016/j.laa.2016.06.029

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 切頂正4,6,8面体上の離散ソボレフ不等式の最良定数2015

    • Author(s)
      亀高惟倫,山岸弘幸,永井敦,渡辺宏太郎,武村一雄
    • Journal Title

      日本応用数理学会論文誌

      Volume: 25 Pages: 135-150

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The Best Cosntant of Discrete Sobolev Inequality on the C60 Fullerene Buckyball2015

    • Author(s)
      Y. Kametaka, A. Nagai, H. Yamagishi, K. Takemura and K. Watanabe
    • Journal Title

      Journal of Physical Society of Japan

      Volume: 84 Issue: 7 Pages: 074004-074004

    • DOI

      10.7566/jpsj.84.074004

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Sobolev inequality of free boundary value problem for (-1)M(d/dx)(2M)2015

    • Author(s)
      K. Takemura, A. Nagai, Y. Kametaka, K. Watanabe, H. Yamagishi
    • Journal Title

      J. of Inequality and Appl.

      Volume: 2015 Issue: 1 Pages: 1-20

    • DOI

      10.1186/s13660-015-0568-9

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] The Best Cosntants of Discrete Sobolev Inequalities on Mobius Ladder2014

    • Author(s)
      Kazuo Takemura
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: Volume 86, Number 2 Pages: 233-248

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Best Constant of Three Kinds of Discrete Sobolev Inequalities on Regular Polyhedron2013

    • Author(s)
      Hiroyuki Yamagishi, Yoshinori Kametaka, Kohtaro Watanabe, Atsushi Nagai and Kazuo Takemura
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: Volume 36, No. 1 Pages: 253-268

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Complete low-cut filter and the best constant of Sobolev inequality2013

    • Author(s)
      Hiroyuki Yamagishi, Yoshinori Kametaka, Atsushi Nagai, Kohtaro Watanabe and Kazuo Takemura
    • Journal Title

      Japan Society for Industrial and Applied Mathematics

      Volume: Volume 5 Pages: 33-36

    • NAID

      130003371118

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The best estimation corresponding to continuous model of Thomson cable2013

    • Author(s)
      Hiroyuki Yamagishi, Yoshinori Kametaka, Atsushi Nagai, Kohtaro Watanabe and Kazuo Takemura
    • Journal Title

      Japan Society for Industrial and Applied Mathematics

      Volume: Volume 5 Pages: 53-56

    • NAID

      130003371123

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] C60フラーレン上の離散ソボレフ不等式の最良定数2015

    • Author(s)
      亀高 惟倫
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      イーグレ姫路
    • Year and Date
      2015-03-05
    • Related Report
      2014 Research-status Report
  • [Presentation] 重み付きd-有限正則グラフ上の離散ソボレフ不等式の最良定数

    • Author(s)
      武村一雄
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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