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Various functional inequalities and their applications to the variational problems

Research Project

Project/Area Number 24840024
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionGifu University

Principal Investigator

WADADE Hidemitsu  岐阜大学, 教育学部, 助教 (00466525)

Project Period (FY) 2012-08-31 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords関数不等式 / 楕円型偏微分方程式 / 変分問題
Research Abstract

Our main purpose of the research lies in studying Sobolev type inequalities and the corresponding variational problems. Especially, we concern the critical embeddings which appear in Trudinger-Moser type inequalities, Gagliardo-Nirenberg type interpolation inequalities and so on. In a period of this fund, we investigated the existence of maximizer associated with the Trudinger-Moser type inequalities of the scaling invariant form obtained by Adachi-Tanaka in 1999, and actually proved the existence of a maximizer. On the other hand, it was known that the similar type Trudinger-Moser inequalities on the whole space which do not satisfy the scaling invariance. Ishiwata (2010) proved that the existence of maximizers for this inequality heavily depends on the dimension. Based on this fact, we considered the variational structure and clarified the relation between the scaling invariance and the existence of a maximizer.

Report

(3 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • Research Products

    (19 results)

All 2014 2013 2012

All Journal Article (15 results) (of which Peer Reviewed: 8 results) Presentation (4 results)

  • [Journal Article] On the sharp constant for the weigh ted Trudinger-Moser type inequali ty of the scaling invariant form2014

    • Author(s)
      Michinori Ishiwata, Makoto N akamura, and Hidemitsu Wadade
    • Journal Title

      Annales del'Institut Henri Poinca re/Analyse non lineaire

      Volume: 31 Pages: 297-314

    • Related Report
      2013 Final Research Report
  • [Journal Article] On the sharp constant for the weighted Trudinger-Moser type inequality of the scaling invariant form2014

    • Author(s)
      Michinori Ishiwata, Makoto Nakamura, Hidemitsu Wadade
    • Journal Title

      Annales de l'Institut Henri Poincare/Analyse non lineaire

      Volume: 31 Pages: 297-314

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalizat ions of the logarithmic Hardy ine quality in critical Sobolev-Lorentz spaces2013

    • Author(s)
      Shuji Machihara, Tohru Ozawa, and Hidemitsu Wadade
    • Journal Title

      Journal of Inequalities a nd Applications

    • Related Report
      2013 Final Research Report
  • [Journal Article] Quantitati ve estimates of embedding consta nts for Gagliardo-Nirenberg inequ alities on critical Sobolev-Besov-L orentz spaces2013

    • Author(s)
      Hidemitsu Wadade
    • Journal Title

      Journal of Fourier Analysis and Applications

      Volume: 19 Pages: 1029-1059

    • Related Report
      2013 Final Research Report
  • [Journal Article] Hardy type inequalities on balls2013

    • Author(s)
      Shuji Machihara, Tohru Ozawa, and Hidemitsu Wadade
    • Journal Title

      Tohoku Ma thematical Journal

      Volume: 65 Pages: 321-330

    • NAID

      130005574219

    • Related Report
      2013 Final Research Report
  • [Journal Article] On the Gagliardo-Nirenberg type inequality in the critical Sobolev- Morrey space2013

    • Author(s)
      Yoshihiro Sawano, and Hidemitsu Wadade
    • Journal Title

      Journal of Fourier Analysis and Applications

      Volume: 19 Pages: 20-47

    • Related Report
      2013 Final Research Report
  • [Journal Article] Hardy type inequalities on balls2013

    • Author(s)
      Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 65 Pages: 321-330

    • NAID

      130005574219

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces2013

    • Author(s)
      Shuji Machihara,Tohru Ozawa,Hidemitsu Wadade
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 381 Pages: 1-14

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space2013

    • Author(s)
      Yoshihiro Sawano, Hidemitsu Wadade
    • Journal Title

      Journal of Fourier Analysis and Applications

      Volume: 19 Issue: 1 Pages: 20-47

    • DOI

      10.1007/s00041-012-9223-8

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hardy type inequalities on balls2013

    • Author(s)
      Shuji Machimara, Tohru Ozawa, Hidemitsu Wadade
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 未定

    • NAID

      130005574219

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sharp constant for the weighted Trudinger-Moser type inequality of the scaling invariant form2013

    • Author(s)
      Michinori Ishiwata, Makoto Nakamura, Hidemitsu Wadade
    • Journal Title

      Annales de l’Institut Henri Poincare / Analyse non lineaire

      Volume: 未定

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimizing problems for t he Hardy-Sobolev type inequality with the singularity on the boun dary2012

    • Author(s)
      Chang-Shou Lin, and Hidemitsu Wadade
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 64 Pages: 79-103

    • Related Report
      2013 Final Research Report
  • [Journal Article] Optimal embeddings on critical S obolev-Lorentz spaces into general ized Morrey spaces2012

    • Author(s)
      Tomoyuki Suzuki, and Hidemitsu Wadade
    • Journal Title

      Advances in Mathematical Sciences and Applic ations

      Volume: 22 Pages: 225-238

    • Related Report
      2013 Final Research Report
  • [Journal Article] MINIMIZING PROBLEMS FOR THE HARDY-SOBOLEV TYPE INEQUALITY WITH THE SINGULARITY ON THE BOUNDARY2012

    • Author(s)
      Chang-Shou Lin, Hidemitsu Wadade
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 64 Issue: 1 Pages: 79-103

    • DOI

      10.2748/tmj/1332767341

    • NAID

      130005128506

    • ISSN
      0040-8735, 2186-585X
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal embeddings on critical Sobolev- Lorentz spaces into generalized Morrey spaces2012

    • Author(s)
      Tomoyuki Suzuki, Hidemitsu Wadade
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 22 Pages: 225-238

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Logarithmic Hard y inequalities on Sobolev-Lorentz -Zygmund spaces in the limiting case2013

    • Author(s)
      和田出秀光
    • Organizer
      日本数学会実函数論分科会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Logarithmic Hardy inequalities on Sobolev-Lorentz-Zygmund spaces in the limiting case2013

    • Author(s)
      Hidemitsu Wadade
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 種々の関数空間における臨界型Sobolev不等式について2012

    • Author(s)
      和田出秀光
    • Organizer
      日本数学会実函数論分科会
    • Place of Presentation
      東京理科大学 (特別講演)
    • Year and Date
      2012-03-29
    • Related Report
      2013 Final Research Report
  • [Presentation] On a singular gap between Sobolev-Besov-Lorentz spaces in the limiting case2012

    • Author(s)
      Hidemitsu Wadade
    • Organizer
      Harmonic Analysis and its Applications at Tokyo 2012
    • Place of Presentation
      Tokyo, Japan, Tokyo Metropolitan University
    • Related Report
      2012 Annual Research Report

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Published: 2012-11-27   Modified: 2019-07-29  

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