The Best Constant of Sobolev Inequalities-from continuous to discrete

• 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
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 応用数学 / ソボレフ不等式 / 最良定数 / 離散化 / 正多面体 / 熱作用素 / 楕円θ関数 / 境界値問題 / グリーン関数 / 離散 / 再生核 / ベルヌーイ多項式 / 超幾何関数

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] Elliptic theta function and the best constants of Sobolev-type inequalities (2012)
  • Author(s): H.Yamagishi, Y.Kametaka, A.Nagai, K.Watanabe, K.Takemura
  • Journal Title: JSIAM Letters Volume: 4 Pages: 1-4
  • NAID: 130002129398
  • Peer Reviewed
• [Journal Article] The best constant of discrete Sobolev inequality corresponding to a bending problem of a string (2012)
  • Author(s): H.Yamagishi, A.Nagai, K.Watanabe, K.Takemura, Y.Kametaka
  • Journal Title: Kumamoto Journal of Mathematics Volume: 25 Pages: 1-15
  • NAID: 110009930106
  • Peer Reviewed
• [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 Clamped Boundary Value Problem (2011)
  • Author(s): K.Watanabe, Y.Kametaka, H.Yamagishi, A.Nagai, K.Takemura
  • Journal Title: Boundary Value Problems Vol.2011(to appear)
  • 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: (掲載確定)
  • Peer Reviewed
• [Journal Article] The best constant of Sobolev inequality corresponding to a bending problem of a beam on a half line (2011)
  • Author(s): K.Takemura, Y.Kametaka, K.Watanabe, A.Nagai, H.Yamagishi
  • Journal Title: Far East Journal of Applied Mathematics Volume: (掲載確定)
  • 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
  • NAID: 120006309462
  • 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
  • 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. 33 Pages: 253-280
  • NAID: 120006309462
  • 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 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 e-2009 Pages: 621-635
  • Peer Reviewed
• [Journal Article] The best constant of discrete Sobolev inequality (2009)
  • Author(s): 永井敦, 亀高惟倫, 渡辺宏太郎
  • Journal Title: J.Phys.A 42
  • Peer Reviewed
• [Journal Article] The best constant of discrete Sobolev inequality (2009)
  • Author(s): A.Nagai
  • Journal Title: Journal of Physics A 42
  • Peer Reviewed
• [Journal Article] Giambelli's formula and the best constant of Sobolev inequality in ine dimensional Euclidean space (2009)
  • Author(s): Y.Kametaka
  • Journal Title: Scienticae Mathematicae Japonicae e-2009 Pages: 621-635
  • 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
  • Journal Title: 日本応用数理学会論文誌 19 Pages: 489-518
  • Peer Reviewed
• [Journal Article] (-l)^M(d/dx)^2Mに対する両端自由端境界値問題と対応するソボレフ不等式の最良定数 (2008)
  • Author(s): 武村一雄
  • Journal Title: 日本応用数理学会論文誌 18 Pages: 41-64
  • Peer Reviewed
• [Journal Article] Diserete Bernoulli Polynomials and the best constant of Sobolev inequality (2008)
  • Author(s): A. Nagai
  • Journal Title: Funkcialaj Ekvacioj 51 Pages: 307-327
  • Peer Reviewed
• [Journal Article] The best constant of Sobolev inequality on a bounded interval (2008)
  • Author(s): K. Watanabe
  • Journal Title: Journal of Mathematical Analysis and Applications 340 Pages: 699-706
  • 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
• [Presentation] The best constant of Sobolev inequalities (2008)
  • Author(s): Atsushi Nagai
  • Organizer: Symmetries and Integrability of Difference Equations 8
  • Place of Presentation: サンタテールカナダ
  • Year and Date: 2008-06-28