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2010 Fiscal Year Self-evaluation Report

Viscosity solution theory for fully nonlinear equations and its applications

Research Project

  • PDF
Project/Area Number 20340026
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSaitama University

Principal Investigator

KOIKE Shigeaki  Saitama University, 大学院・理工学研究科, 教授 (90205295)

Project Period (FY) 2008 – 2010
Keywords粘性解 / 完全非線形方程式 / 最大値原理 / ハルナック不等式 / 比較原理
Research Abstract

完全非線形2階楕円型偏微分方程式の粘性解の性質を研究する。
(1)一様楕円型方程式の場合に、一階微分項に非有界係数が時のLp粘性解の弱ハルナック不等式を導く。また、一階微分項が一次以上の増大度を持つ場合にも研究する。
(2)最大値原理・弱ハルナック不等式の応用として、粘性解の強最大値原理や局所最大値原理を導く。更に、Phagmen-Lindelofの定理等のLp粘性解の定性的性質を研究する。
(3)退化楕円型方程式の場合に、一階微分に関して一次以上の増大度がある時の非有界領域での粘性解の比較原理を導く。更に、方程式系等への一般化の研究もする。

  • Research Products

    (12 results)

All 2011 2010 2009 2008

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Presentation (6 results) Book (1 results)

  • [Journal Article] Weak Harnack inequality for fully nonlinear PDEs with superlinear growth terms in Du2010

    • Author(s)
      S.Koike
    • Journal Title

      数理解析研究所講究録「微分方程式の粘性解理論とその周辺」 1695巻

      Pages: 139-147

  • [Journal Article] Recent developments on maximum principle for Lp-viscosity solutions of fully nonlinear elliptic/parabolic PDEs.2009

    • Author(s)
      S.Koike
    • Journal Title

      Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions(World Sci.Publ.)

      Pages: 131-153

    • Peer Reviewed
  • [Journal Article] Remarks on the Phragmen-Lindelof theorem for Lp-viscosity solutions of fully nonlinear PDEs with unbounded ingredients. Electron.2009

    • Author(s)
      S.Koike, K.Nakagawa
    • Journal Title

      J.Differential Equations 146巻

      Pages: 1-14

    • Peer Reviewed
  • [Journal Article] Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients.2009

    • Author(s)
      S.Koike, A.Swiech
    • Journal Title

      J.Math.Soc.Japan 61巻

      Pages: 723-755

    • Peer Reviewed
  • [Journal Article] Existence of strong solutions of Pucci extremal equations with superlinear growth in Du.2009

    • Author(s)
      S.Koike, A.Swiech
    • Journal Title

      J.Fixed Point Theory Appl. 5巻

      Pages: 291-304

    • Peer Reviewed
  • [Presentation] On viscosity solutions of fully nonlinear elliptic PDE with measurable and unbounded ingredients2011

    • Author(s)
      小池茂昭
    • Organizer
      Nonlinear PDE's, Valparaiso
    • Place of Presentation
      Chile
    • Year and Date
      2011-01-14
  • [Presentation] 完全非線形楕円型偏微分方程式のLp粘性解について2010

    • Author(s)
      小池茂昭
    • Organizer
      研究集会「微分方程式の総合的研究
    • Place of Presentation
      京都大学
    • Year and Date
      20101218-20101219
  • [Presentation] On the weak Harnack inequality for fully nonlinear PDEs with unbounded ingredients2010

    • Author(s)
      小池茂昭
    • Organizer
      研究集会"Viscosity methods and nonlinear PDE"
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-07-21
  • [Presentation] Weak Harnack inequality for fully nonlinear PDEs with unbounded ingredients2010

    • Author(s)
      小池茂昭
    • Organizer
      Positivity : A key to fully nonlinear equations Conference
    • Place of Presentation
      Salerno(Italy)
    • Year and Date
      2010-06-02
  • [Presentation] Weak Harnack inequality for Lp-viscosity solutions of fully nonlinear PDEs with unbounded ingredients2009

    • Author(s)
      小池茂昭
    • Organizer
      The Second Chile-Japan Workshop on Elliptic and Parabolic Equations
    • Place of Presentation
      明治大学
    • Year and Date
      2009-12-02
  • [Presentation] Weak Harnack inequality for Lp-viscosity solutions of fully nonlinear elliptic PDEs with unbounded ingredients2009

    • Author(s)
      小池茂昭
    • Organizer
      The Second International Conference of Reaction Diffusion Systems and Viscosity Solution.
    • Place of Presentation
      Providence University・台湾
    • Year and Date
      2009-07-18
  • [Book] International Conference for the 25th Anniversary of Viscosity Solutions, GAKUTO International Series, Mathematical Sciences and Applications, 30巻2008

    • Author(s)
      edited by Y.Giga, K.Ishii, S.Koike, T.Ozawa, N.Yamada
    • Publisher
      Gakkotosho

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Published: 2012-02-13   Modified: 2016-04-21  

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