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2013 Fiscal Year Final Research Report

New developements of the regularity theory on the solutions to the Liouville-Gelfand type problems and the related parabolic dynamics

Research Project

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Project/Area Number 24654043
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionOsaka City University

Principal Investigator

TAKAHASHI Futoshi  大阪市立大学, 理学(系)研究科(研究院), 教授 (10374901)

Co-Investigator(Kenkyū-buntansha) SUGIYAMA Yoshie  九州大学, 大学院・数理学研究院, 教授 (60308210)
SATO Yohei  埼玉大学, 理工学研究科, 講師 (00465387)
Project Period (FY) 2012-04-01 – 2014-03-31
Keywords極解 / 非線形固有値問題 / 放物型力学系 / 特異解
Research Abstract

The aim of this research program is to solve the long open problem concerning the regularity and singularity of extremal solutions to the Liouville-Gelfand type nonlinear eigenvalue problems in a unified way, with no assumptions of the domains or the symmetry of solutions, by combining ideas from the geometric variational problems and the techniques of nonlnear analysis.
The research outputs by the research group in the period of the program, 2012-2013, are the following: 20 published papers (including accepted papers), 7 talks at Math. Soc. Japan, 21 talks by the reseach representative at seminars, including abroad.

  • Research Products

    (17 results)

All 2014 2013 2012 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (4 results) Remarks (2 results)

  • [Journal Article] Asymptotic behavior of least energy solutions for a 2D nonlinear Neumann problem with large exponent2014

    • Author(s)
      F.Takahashi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 411, no.1 Pages: 95-106

    • DOI

      10.1016/j.jmaa.2013.09.044

    • Peer Reviewed
  • [Journal Article] Multiple peak aggregations for the Keller-Segel system2014

    • Author(s)
      Y. Seki, Y. Sugiyama, J.J.L. Velazquez
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 411, no.1 Pages: 95-106

    • DOI

      10.1016/j.jmaa.2013.08.065

    • Peer Reviewed
  • [Journal Article] Morse indices and the number of blow up points of blowing-up solutions for a Liouville equation with singular data2013

    • Author(s)
      F. Takahashi
    • Journal Title

      Proceedings of the 9th AIMS (Orlando, Florida) International Conference on ``Dynamica Systems, Differential Equations and Applications" Discrete and Continuous Dynamical Systems, Supplement

      Pages: 729-736

    • Peer Reviewed
  • [Journal Article] Some identities of Green's function for the polyharmonic operator with the Navier boundary conditions and its applications2013

    • Author(s)
      F. Takahashi
    • Journal Title

      Mathematische Nachrichten

      Volume: 286, no.2-3 Pages: 306-319

    • DOI

      10.1002/mana.201100236

    • Peer Reviewed
  • [Journal Article] Nonexistence of multi-bubble solutions for a higher order mean field equation on convex domains2013

    • Author(s)
      F. Takahashi
    • Journal Title

      ``Geometric Properties of Parabolic and Elliptic PDE's". A. Alvino, R. Magnanini, S. Sakaguchi, (ed.). Springer INdAM Ser.

      Volume: Vol.2 Pages: 283-293

    • DOI

      10.1007/978-88-407-2841-8_18

    • Peer Reviewed
  • [Journal Article] On the number of maximum points of least energy solutions to a two-dimensional H¥'enon equation with large exponent2013

    • Author(s)
      F. Takahashi
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 12, no.3 Pages: 1237-1241

    • DOI

      10.3934/cpaa.2013.12.1237

    • Peer Reviewed
  • [Journal Article] Global solutions to a chemotaxis system with non-diffusive memory2013

    • Author(s)
      Y. Sugiyama, Y. Tsutsui, J.J.L. Velazquez
    • Volume
      26
    • Pages
      319-352
    • DOI

      10.1088/0951-7715/26/2/319

    • Peer Reviewed
  • [Journal Article] On the multiple existence of semi-positive solutions for a nonlinear Schrodinger system2013

    • Author(s)
      Y. Sato, Z.Q. Wang
    • Journal Title

      Ann. Inst. H. Poincare Anal. Non Lineaire

      Volume: 30 Pages: 1-22

    • DOI

      10.1016/j.anihpe.2012.05.002

    • Peer Reviewed
  • [Journal Article] Extremal solutions to Liouville-Gelfand type elliptic problems with nonlinear Neumann boundary conditions

    • Author(s)
      F.Takahashi
    • Journal Title

      Contemporary Math

      Volume: (to appear in Commun)

    • Peer Reviewed
  • [Journal Article] Continuum spectrum for the linearized extremal eigenvalue problem with boundary reactions

    • Author(s)
      F.Takahashi
    • Journal Title

      Bohemica

      Volume: (to appear) Math (Equadiff 13 proceedings)

    • Peer Reviewed
  • [Journal Article] On the location of two blow up points on an annulus for the mean field equation

    • Author(s)
      M. Grossi, F. Takahashi
    • Journal Title

      Comptes Rendus Mathematique

      Volume: (to appear)

    • Peer Reviewed
  • [Presentation] Extremal solutions to Liouville-Gelfand type elliptic problems with nonlinear Neumann boundary conditions2014

    • Author(s)
      高橋太
    • Organizer
      日本数学会春季年会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-17
  • [Presentation] Continuum spectrum for the linearized extremal eigenvalue problem with boundary reactions2014

    • Author(s)
      高橋太
    • Organizer
      日本数学会春季年会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-17
  • [Presentation] Asymptotic behavior of least energy solutions for a 2D nonlinear Neumann problem with large exponent2013

    • Author(s)
      高橋太
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-26
  • [Presentation] 大きな指数を持つ2次元Henon方程式の最小エネルギー解の最大点について2012

    • Author(s)
      高橋太
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-19
  • [Remarks] 研究代表者高橋のプレプリントは大阪市立大学数学研究所(OCAMI)のOCAMI Preprint Series

    • URL

      http://www.sci.osaka-cu.ac.jp/math/OCAMI/preprint/index_13.html

  • [Remarks] 研究分担者:杉山由恵のHP

    • URL

      http://www2.math.kyushu-u.ac.jp/~sugiyama/index.htm

URL: 

Published: 2015-06-25   Modified: 2018-05-11  

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