On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equations

论经典不等式的改进及其在非线性简并椭圆方程中的应用

• 批准号: 20540153
• 负责人: HORIUCHI Toshio
• 金额: $ 2.75万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540153/
• 关键词: 重み付きソボレ不等式; 重み付きハーディ不等式; CKN型不等式; ミッシング・ターム; 退化楕円型方程式; 非線形変分問題; 楕円型偏微分方程式; ソボレフ不等式; ハーディ不等式; 退化楕円型問題; ミッシングターム; 対称性の破れ; 非線形楕円型方程式; 変分問題; 退化楕円型; バーディ不等式

(1) The classical Hardy-Sobolev inequalities were improved by finding out sharp missing terms and the best constants.(2) By making effective use of the improved Hardy-Sobolev inequalities, nonlinear problems were successfully studied.(3) By a linearization method the symmetry breaking of the Caffarelli-Khon-Nirenberg type inequalities were investigated to make clear its mechanism.(4) The operators on the Orlicz with a variable exponent p(x) were studied using the Hardy inequalities.

(1)通过找出明显的缺失项和最佳常数，改进了经典Hardy-Sobolev不等式。(2)利用改进的Hardy-Sobolev不等式，成功地研究了非线性问题。(3)采用线性化方法研究了Caffarelli-Khon-Nirenberg型不等式对称性破缺的机理。(4)利用Hardy不等式研究了变指数p(x)的Orlicz算子。

项目成果

Liouville type theorem associated with the wave equation

与波动方程相关的刘维尔型定理

• 发表时间: 2011
• 期刊: Math. J. Ibaraki Univ.
• 作者: 岡田憲相;青柳美輝;鈴木智成;青柳美輝 岡田憲相;小森洋平;K. Shimomura
• 通讯作者: K. Shimomura

Pointwise multipliers of Orlicz spaces

• DOI: 10.1007/s00013-010-0160-y
• 发表时间: 2010-07
• 期刊: Archiv der Mathematik
• 影响因子: 0.6
• 作者: L. Maligranda;E. Nakai

Singular and fractional integral operators on Campanato spaces with variable growth conditions

• DOI: 10.1007/s13163-009-0022-y
• 发表时间: 2010-07
• 期刊: Revista Matemática Complutense
• 作者: E. Nakai

Caloric morphisms for rotation invariantmetrics

旋转不变度量的热量态射

• 发表时间: 2010
• 期刊: Hiroshima Math.J. Vol.40 No.3
• 作者: Nishio;Masaharu shimomura;Katsunori
• 通讯作者: Katsunori

Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations

• DOI: 10.14492/hokmj/1300108399
• 发表时间: 2011-02
• 期刊: Hokkaido Mathematical Journal
• 影响因子: 0.5
• 作者: E. Nakai;Tsuyoshi Yoneda