Potential analysis

潜力分析

• 批准号: 15340046
• 负责人: AIKAWA Hiroaki
• 金额: $ 5.38万
• 依托单位: Hokkaido University (2005-2006)Shimane University (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340046/
• 关键词: capacity density condition; harmonic measure; harmonic function; uniform domain; Bergman space; Dirac equation; Sobolev function; parabolic equation; 関数微分方程式; 内部一様領域; Carleson評価; Fatou定理; 熱方程式

・Under the capacity density condition, we characterize uniform domains, inner uniform domains and John domains in terms of the boundary Hamack principle and estimates of harmonic measure.・We study the bounday behavior of non-integrable kernel and derive the Fatou type theorem and Littlewood type theorem.・We show the 3G-inequality for inner uniform domains. We construct a domain whose Martin boundary and topological boundary coincide, and yet the Cranston-McConnell inequality, and as a result, the 3G- inequality fail to hold in case the dimension is greater than or equal 3.・We show the equivalence between the boundary Hamack principle and the Carleson estimate.・For a smooth doimain in the Euclid space. we show the boundary Harnack principle for p-harmonic func- tion.・We give the Carleson estomates for p-harmonic functions.・We give conditions for the p-Dirichlet solution of a Holder continuos boundary function to be Hoder continuos up tp the boundary.・We study the Martin boundary of a John domain. By the John constant, we estimate the number of minimal Martin boundary points over a topological boundary.

·在容量密度条件下，利用边界Hamack原理和调和测度的估计刻画了一致域、内一致域和John域.研究了不可积核的有界性态，得到了Fatou型定理和Littlewood型定理.证明了内一致整环的3G-不等式。我们构造了一个Martin边界与拓扑边界重合的区域，但Cranston-McConnell不等式成立，结果当维数大于或等于3时，3G-不等式不成立。·我们证明了边界Hamack原理和Carleson估计之间的等价性。·对于欧几里得空间中的光滑域。我们证明了p-调和函数的边界Harnack原理。·我们给出p-调和函数的Carleson估计。·给出了保持器连续边界函数的p-Dirichlet解在边界上是Hoder连续的条件.研究了John整环的Martin边界.利用John常数估计了拓扑边界上极小Martin边界点的个数。

项目成果

Toeplitz operators and Carleson measures on parabolic Bergman spaces

抛物线伯格曼空间上的托普利茨算子和卡尔森测度

• 发表时间: 2007
• 期刊: Hokkaido Mathematical Journal 36
• 作者: M. Nishio;N. Suzuki;M. Yamada
• 通讯作者: M. Yamada

Martin boundary of a fractal domain

分形域的 Martin 边界

• 发表时间: 2003
• 期刊: Potential Anal. 18
• 作者: H.Aikawa;T.Lundh;T.Mizutani
• 通讯作者: T.Mizutani

Martin boundary and boundary Harnack principle for non-smooth domains

非光滑域的 Martin 边界和 Harnack 边界原理

• 发表时间: 2005
• 期刊: Amer.Math.Transl. 215
• 作者: H.Aikawa;Skanmugalingam;H.Aikawa
• 通讯作者: H.Aikawa

Mean value densities for temperatures.

温度的平均值密度。

• 发表时间: 2003
• 期刊: Colloq.Math. 98
• 作者: N.Suzuki;N.A.Watson
• 通讯作者: N.A.Watson

A system of nonlinear nonlocal transport equations related to muscle contraction mechanism

与肌肉收缩机制相关的非线性非局部传输方程组

• 期刊: Adv.Math.Sci.Appl. (発表予定)
• 作者: T.Ichinose;D.Fan;G.G.Gundersen;佐藤 秀一;G.G.Gundersen;Y.Kanjin;Y.Kanjin;T.Ichinose;N.Kato;N.Kato
• 通讯作者: N.Kato