Potential theoretical reserch for nonlinear partial differential equations

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540196
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Fukuyama Heisei University (2010-2011); Fukuyama University (2008-2009)
• Principal Investigator: ONO Takayori Fukuyama University (60289270)
• Project Period (FY): 2008 – 2011
• Keywords: 非線形偏微分方程式 / ポテンシャル論 / 函数空間

Research Abstract

p-Laplace方程式(1<p<∞)を含む2階楕円型非線形偏微分方程式に対するポテンシャル論的研究を発展させる.またそれらと並行して,関数空間,特に、変動関数指数をもつ関数空間を考察し,ポテンシャル論的議論の進展に寄与する研究を行う.

Research Products

• [Journal Article] Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent (2010)
  • Author(s): Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
  • Journal Title: Journal of Mathematical Analysis and Applications
• [Journal Article] Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms (2008)
  • Author(s): T.Ono
  • Journal Title: Ann.Acad.Sci.Fenn..Math.
• [Journal Article] Lindelof theorems for monotone Sobolev functions with variable exponent (2008)
  • Author(s): T.Futamura, T.Shimomura
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci
• [Presentation] Removable sets for continuous solutions of quasilinear elliptic equations with lower order terms (2009)
  • Author(s): T.Ono
  • Organizer: International Workshop on Potential Theory
  • Year and Date: 20090000
• [Presentation] 変動指数をもつ関数空間におけるリースポテンシャルのハーディー型不等式
  • Author(s): 二村俊英、水田義弘、下村哲
  • Organizer: 日本数学会2009年度年会
• [Presentation] Hardy's inequality in Orlicz-Sobolev spaces of variable exponent
  • Author(s): 水田義弘、中井英一、大野貴雄、下村哲
  • Organizer: 日本数学会2010年度秋季総合分科会