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偏微分方程式の局所および大域解析

Research Project

Project/Area Number 08640167
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionSaitama University

Principal Investigator

櫻井 力  埼玉大学, 理学部, 助教授 (40187084)

Co-Investigator(Kenkyū-buntansha) 柳井 久江  埼玉大学, 理学部, 助手 (10008865)
福井 敏純  埼玉大学, 理学部, 助教授 (90218892)
小池 茂昭  埼玉大学, 理学部, 助教授 (90205295)
奥村 正文  埼玉大学, 理学部, 教授 (60016053)
辻岡 邦夫  埼玉大学, 理学部, 教授 (30012412)
Project Period (FY) 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1996: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsSymplectic characteristic / 擬微分作用素 / 解析的準楕円性 / 局所可解性 / CR多様体 / 最適制御問題 / Bellman方程式 / 粘性解
Research Abstract

(1)研究代表者櫻井はSymplecticな特性集合を持つ偏微分方程式の超局所的性質について研究を行なった.Symplecticな特性集合を持つ作用素をHeisenberg群にモデル化し,その上の調和解析の理論を構築することにより方程式の解が持つ特異性について詳細に調べた.具体的には,Sub-elliptic条件をみたす不変作用素のParametricを(1/2,1/2)タイプの擬微分作用素として実現し,そののち,Sub-elliptic条件を満たさない作用素に対して摂動論を展開した.この研究は“Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics" (Bnach Center Publications,33,1996,315-335)にまとめられている.
(2)分担者奥村は主に複素射影空間のある種のCR-部分多様体の上でラプラシアンの固有値とスカラー曲率との関係について研究し,Y.W.Choe-M.Okumura:Scalar curvature of a certain CR-submamifold of complex projective space (to appear in Arkev der Math.)に発表した.
(3)分担者小池は決定論的な状態拘束条件下での効用関数の,対応する一階Bellman方程式の境界条件を特徴付け,その下で効用関数が一意的な粘性解であることを示した.(A new formulation of state constraint problems for first-order PDEs,SAIM J.,34(1996))
また,制御集合が状態に依存する場合のBellman方程式の解の一意性のための十分条件を示し,その条件が満たされない場合の例をあげた.

Report

(1 results)
  • 1996 Annual Research Report
  • Research Products

    (6 results)

All Other

All Publications (6 results)

  • [Publications] T.Sakurai: "Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics" Banach Center Publications,Singularities and Differential Equations. 33. 315-335 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.-W.Choe,M.Okumura: "Scalar curvature of a certain CR-manifold of complex projective space" Arkev der Mathematik. (to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Ishii,S.Koike: "A new formulation of state constraint problems for first-order PDEs" SIAM Journal,Control and Optimization. 34. 554-571 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] S.Koike: "On the Bellman equations with varying control" Bulletin of the Australian Mathematical Society. 53. 51-62 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Fukui: "Seeking invariants for blow-analytic equivalence" Compositio Mathematica (to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Fukui: "Newton polygon and topology of zero loci of real polynomials" Journal of the London Mathematical Society. (to appear).

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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