The Best Constant of Sobolev Inequalities-from continuous to discrete

2010 Fiscal Year Self-evaluation 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 Nihon University, 生産工学部, 准教授 (90304039)
• Project Period (FY): 2008 – 2011
• Keywords: 応用数学

Research Abstract

(1)20世紀の微分方程式論の要であるソボレフ不等式の最良定数を境界値問題のグリーン関数をベースにして求める.
(2)同時にこれまで手がけられていなかったソボレフ不等式の離散化を確立する.

Research Products

• [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 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
  • 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 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