Potential Analysis for Sobolev functions

Sobolev 函数的潜力分析

• 批准号: 14340046
• 负责人: MIZUTA Yoshihiro
• 金额: $ 5.44万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340046/
• 关键词: potential; partial differential equation; polyharmonic functions; monotone functions in the sense of Lebesgue; tangential boundary limits; function space; Sobolev's theorem; variable exponent; ソボレフ関数; ソボレフの不等式; Trudingerの不等式; ルベーグの単調関数; 孤立特異点

・The head Investigator, with the help of T. Shimomura, extended the Fatou theorem for Sobolev's monotone functions in the sense of Lebesgue. In relation with Liouville's theorem and Bocher's theorem for harmonic functions, he investigated isolated singularities for polyharmonic functions. Furthermore, he studied Sobolev's function spaces with variable exponent, and extended Sobolev's theorem in the metric space setting.・T.Shibata studied eigen value problem for elliptic partial differential equations.・H.Usami characterized asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations・T.Nagai treated qualitative properties of solutions to a reaction-diffusion equation with advection modelling chemotaxis.・M.Shiba and M.Masumoto studied circularizable domains on Riemann surfaces.・N.Suzuki and M.Nishio extended Bergman space theory for fractional heat equations.・H.Masaoka showed a condition for the existence of positive harmonic functions with finite Dirichlet integral on Riemann surfaces.・T.Shima and M.Furushima studied analytic compactifications in Fano manifolds.・H.Yoshida investigated the behavior of harmonic functions on cones through minimally thin sets.

·首席调查员，在T. Shimomura在Lebesgue意义下推广了Sobolev单调函数的Fatou定理。在关系刘维定理和Bocher定理的调和函数，他调查孤立奇点的多调和函数。此外，他还研究了变指数的Sobolev函数空间，并在度量空间中推广了Sobolev定理。·T.柴田研究了椭圆型偏微分方程的特征值问题. H.Usami刻画了二阶拟线性常微分方程正解的渐近形式·T.永井处理了具有平流模型趋药性的反应扩散方程解的定性性质。·Shiba和Masumoto研究了黎曼曲面上的可圈化区域。·N.Suzuki和M.西尾将Bergman空间理论推广到分数阶热方程。·H.Masaoka给出了黎曼曲面上具有有限Dirichlet积分的正调和函数存在的条件。·T.Shima和M.Furushima研究了Fano流形中的解析紧化。·H.Yoshida通过极小薄集研究了锥上调和函数的行为。

项目成果

Boundary behavior of monotone Sobolev functions on John domains in a metric space

度量空间中 John 域上单调 Sobolev 函数的边界行为

• 发表时间: 2005
• 期刊: Complex Variables 50・6
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura
• 通讯作者: T.Futamura

Shibata, Tetsutaro: "Precise spectral asymptotics for the Dirichlet problem -u"(t)+g(u(t))=λsin u(t)"J. Math. Anal. Appl.. 267 no.2. 576-598 (2002)

Shibata，Tetsutaro：“狄利克雷问题的精确谱渐近 -u”(t)+g(u(t))=λsin u(t)”J. Math. Anal. Appl.. 267 no.2. 576-598 (2002)

Matsumoto, Makoto: "Hyperbolically maximal domains and fundamental domains for a discontinuous group of conformal automorphisms of a Riemann, surface"Q. J. Math.. 53 no.3. 337-346 (2002)

Matsumoto，Makoto：“黎曼曲面的不连续群共形自同构的双曲最大域和基本域”Q。

Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations

二阶拟线性常微分方程正解的渐近形式

• 发表时间: 2006
• 期刊: Adv. Math. Sci. Appl. (印刷中)
• 作者: Y.Kagei;Y.Ohtsubo;Y.Goto;T.Kobayashi;Y.Ohtsubo;S.Kawashima;藤田敏治;S.Kawashima;T.Fujita;S.Kawashima;H.Hyakutake;K.Ohgane;H.Hyakutake;T.Nakamura;H.Kawasaki;T.Ogawa;S.Iwamoto;T.Ogawa;Y.Ohtsubo;H.Usami
• 通讯作者: H.Usami

Mizuta, Yoshihiro: "Continuity and differentiability for weighted Sobolev spaces"Proc. Amer. Math. Soc.. 130 no.10. 2985-2994 (2002)

Mizuta，Yoshihiro：“加权 Sobolev 空间的连续性和可微性”Proc。