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2008 Fiscal Year Final Research Report

Asymptotic analysis of heat kernels and Green functions and its applications

Research Project

  • PDF
Project/Area Number 17340034
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

MURATA Minoru  Tokyo Institute of Technology, 大学院・理工学研究科, 教授 (50087079)

Project Period (FY) 2005 – 2008
Keywords解析学 / 関数方程式論 / 解析・評価 / 関数解析学 / 確率論
Research Abstract

放物型偏微分方程式に対する初期値・境界値問題の非負値解の一意性定理を応用して、歪積型楕円型方程式のマルチン境界を決定する方法を与えた.また、リーマン多様体上の筒状領域での2階放物型偏微分方程式の非負値解の構造を精力的に研究し、熱核に対する一般的な仮定IU「intrinsic ultracontractivity]の下で任意の非負値解の具体的な積分表示を与えた.さらにIUから[定数関数1が随伴楕円型作用素の小摂動である]ことが従うことも示した.一方、土田哲生とともに周期係数楕円型作用素を研究し、グリーン関数の漸近形を与えるとともに極限吸収原理を示した.

  • Research Products

    (22 results)

All 2009 2008 2007 2006 2005

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (10 results) Book (2 results)

  • [Journal Article] Gradient estimates for the heat equation in the exterior domains under the Neumann boundary condition2009

    • Author(s)
      石毛和弘
    • Journal Title

      Differential Integral Equations 22

      Pages: 401-410

    • Peer Reviewed
  • [Journal Article] Equivalence between the boundary Harnack principle and the Carleson estimate2008

    • Author(s)
      相川弘明
    • Journal Title

      Math. Scad 103

      Pages: 61-76

    • Peer Reviewed
  • [Journal Article] Doubling conditions for harmonic measure in John domains2008

    • Author(s)
      相川弘明, 平田賢太郎
    • Journal Title

      Ann. Inst. Fourier (Grenoble) 58

      Pages: 429-445

    • Peer Reviewed
  • [Journal Article] Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries2007

    • Author(s)
      村田實
    • Journal Title

      J. Functional Anal 245

      Pages: 177-212

    • Peer Reviewed
  • [Journal Article] Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes2007

    • Author(s)
      内山耕平
    • Journal Title

      Electric Journal of Probability 12

      Pages: 138-180

    • Peer Reviewed
  • [Journal Article] Intrinsic ultracontractivity and small perturbation for one dimensional generalized diffusion operators2007

    • Author(s)
      富崎松代
    • Journal Title

      Journal of Functional Analysis 251

      Pages: 289-32

    • Peer Reviewed
  • [Journal Article] Asymptotics of Green functions and the limiting absorption principle for elliptic operators with periodic coefficients2006

    • Author(s)
      村田實, 土田哲生
    • Journal Title

      J. Math. Kyoto Univ 76

      Pages: 713-754

    • Peer Reviewed
  • [Journal Article] Representations of nonnegative solutions for parabolic equations2006

    • Author(s)
      村田實
    • Journal Title

      Advanced Studies in Pure Mathematics 44

      Pages: 283-289

    • Peer Reviewed
  • [Journal Article] Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form2005

    • Author(s)
      村田實
    • Journal Title

      J. Math. Soc. Japan 57

      Pages: 1-27

    • Peer Reviewed
  • [Journal Article] On the hyperbolic length and quasiconformal mappings2005

    • Author(s)
      志賀啓成
    • Journal Title

      Complex Variables 50

      Pages: 123-130

    • Peer Reviewed
  • [Presentation] 複雑領域上の正調和関数2009

    • Author(s)
      相川弘明
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
  • [Presentation] Structure of nonnegative solutions for parabolic equations and perturbation theory for elliptic operators2009

    • Author(s)
      村田實
    • Organizer
      研究集会「Potential Theory and Related Fields」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-17
  • [Presentation] The decay of the solutions for the heat equation with a potential2009

    • Author(s)
      石毛和弘
    • Organizer
      Workshop on Viscosity Solutions and Related Topics
    • Place of Presentation
      サピアタワー・埼玉大サテライトキャンパス
    • Year and Date
      2009-01-30
  • [Presentation] Martin 境界, 境界Harnack原理と擬双曲距離2008

    • Author(s)
      相川弘明
    • Organizer
      第55回幾何学論シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-25
  • [Presentation] フラクタルな境界を持つ領域の等角写像について2007

    • Author(s)
      志賀啓成
    • Organizer
      研究集会「 確率論とPDE」
    • Place of Presentation
      広島大学学士会館
    • Year and Date
      2007-10-15
  • [Presentation] Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries2006

    • Author(s)
      村田實
    • Organizer
      研究集会「Recent Topics of Differential Equations」
    • Place of Presentation
      群馬大学東京オフィス
    • Year and Date
      2006-10-21
  • [Presentation] Characterization of small perturbation of one-dimensional diffusion operators2006

    • Author(s)
      富崎松代
    • Organizer
      研究集会「Recent Topics of Differential Equations」
    • Place of Presentation
      群馬大学東京オフィス
    • Year and Date
      2006-10-21
  • [Presentation] Comformal mappings of invariant components of Kleinian groups2006

    • Author(s)
      志賀啓成
    • Organizer
      The international conference of complex analysis and potential theory
    • Place of Presentation
      Gebze Institute of Technology
    • Year and Date
      2006-09-11
  • [Presentation] Blow-up set for a semilinear heat equation with large diffusion in RN2006

    • Author(s)
      石毛和弘
    • Organizer
      Second Euro-Japanese Workshop on Blow Up
    • Place of Presentation
      Madrid
    • Year and Date
      2006-09-08
  • [Presentation] Boundary estimates of p-harmonic functions in a metric measure space2005

    • Author(s)
      相川弘明
    • Organizer
      研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2005-07-15
  • [Book] 複雑領域上のディリクレ問題- ポテンシャル論の観点から2008

    • Author(s)
      相川弘明
    • Total Pages
      302
    • Publisher
      岩波書店
  • [Book] 楕円型・放物型偏微分方程式2006

    • Author(s)
      村田實、倉田和浩
    • Total Pages
      1-258
    • Publisher
      岩波書店

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Published: 2010-06-10   Modified: 2016-04-21  

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