| Project/Area Number |
15340046
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hokkaido University (2005-2006)
Shimane University (2003-2004) |
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Principal Investigator |
AIKAWA Hiroaki Hokkaido Univ., Fac. of Sci., Professor, 大学院理学研究院, 教授 (20137889)
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| Co-Investigator(Kenkyū-buntansha) |
KUROIWA Daishi Shimane Univ., Dept. of Math., Associate Professor, 総合理工学部, 助教授 (40284020)
MACHIHARA Shuko Shimane Univ., Dept. of Math., Associate Professor, 総合理工学部, 助教授 (20346373)
MIZUTA Yoshihiro Hiroshima Univ., Dept. of Math., Professor, 総合科学部, 教授 (00093815)
SUZUKI Noriaki Nagoya Univ., Grad. Sch. of Math., Associate Professor, 大学院多元数理学科, 助教授 (50154563)
NAKANISHI toshihiro Shimane Univ., Dept. of Math., Professor, 総合理工学部, 教授 (00172354)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 2006: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2005: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | 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 |
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| Research Abstract |
・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.
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