The Best Constant of Sobolev Inequalities-from continuous to discrete

2011 Fiscal Year Final Research Report

• Project/Area Number: 20540138
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nihon University
• Principal Investigator: NAGAI Atsushi 日本大学, 生産工学部, 准教授 (90304039)
• Co-Investigator(Kenkyū-buntansha): KAMETAKA Yoshinori 大阪大学, 大学院・基礎工学研究科, 名誉教授 (00047218)
• Project Period (FY): 2008 – 2011
• Keywords: 応用数学

Research Abstract

We have found the best constants of Sobolev inequalities, which play important roles in the development of differential equations in 20th century, by using Green functions of many kinds of boundary value problems. We also discretize the Sobolev inequalities, which had been unsolved problems.

Research Products

• [Journal Article] 正多面体上の離散ソボレフ不等式の最良定数 (2011)
  • Author(s): 亀高惟倫, 渡辺宏太郎, 山岸弘幸, 永井敦, 武村一雄
  • Journal Title: 日本応用数理学会論文誌 Volume: 21 Pages: 289-308
  • Peer Reviewed
• [Journal Article] The Best Constant of Sobolev Inequality Corresponding To Clamped Boundary Value Problem (2011)
  • Author(s): K. Watanabe, Y. Kametaka, H. Yamagishi, A. Nagai, K. Takemura
  • Journal Title: Boundary Value Problems Volume: Vol.2011 Pages: 875057, 17
  • Peer Reviewed
• [Journal Article] The best constant of Sobolev Inequality corresponding to a bending problem of a beam on an interval (2009)
  • Author(s): K. Takemura, H. Yamagishi, Y. Kametaka, K. Watanabe, A. Nagai
  • Journal Title: Tsukuba J. Math Volume: 33 Pages: 253-280
  • Peer Reviewed
• [Journal Article] 弾性基盤上の張力をかけた棒のたわみの2点境界値問題と対応するソボレフ不等式の最良定数 (2009)
  • Author(s): 山岸弘幸、亀高惟倫、武村一雄、渡辺宏太郎、永井敦
  • Journal Title: 日本応用数理学会論文誌 Volume: 19 Pages: 489-518
  • Peer Reviewed
• [Journal Article] Giambelli's formula and the best constant of Sobolev inequality in ine dimensional Euclidean space (2009)
  • Author(s): Y. Kametaka, A. Nagai, K. Watanabe, K. Takemura, H. Yamagishi
  • Journal Title: Scienticae Mathematicae Japonicae Volume: e-2009 Pages: 621-635
  • Peer Reviewed
• [Journal Article] The best constant of discrete Sobolev inequality (2009)
  • Author(s): A. Nagai, Y. Kametaka, K. Watanabe
  • Journal Title: J. Phys. A Volume: 42 Pages: 454014(12)
  • Peer Reviewed
• [Presentation] 正多面体に対応する離散ソボレフ不等式の最良定数 (2011)
  • Author(s): 山岸弘幸
  • Organizer: 日本応用数理学会
  • Place of Presentation: 電気通信大学
  • Year and Date: 2011-03-07
• [Presentation] 3次元球における重調和作用素と対応するソボレフ不等式の最良定数 (2009)
  • Author(s): 永井敦
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24