Research of the potential theory for elliptic type or parabolic type in unbounded domains and its consideration in stochastic analysis
| Project/Area Number |
19540166
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Chiba University |
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Principal Investigator |
MIYAMOTO Ikuko Chiba University, 大学院・理学研究科, 教授 (00009606)
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| Co-Investigator(Kenkyū-buntansha) |
TANEMURA Hideki 千葉大学, 大学院・理学研究科, 教授 (40217162)
SHIMOMURA Katunori 茨城大学, 理学部, 准教授 (00201559)
YOSHIDA Hidenobu 千葉大学, 名誉教授 (60009280)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 複素解析 / 非有界領域 / ディリクレ問題 / 熱方程式 / ポアソン核 / ガウスワイヤストラス核 / 調和関数 / temperature / minimum princinle / minimum principle / コーン / シリンダー / minimally thin sets / rarefied sets |
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| Research Abstract |
Our aim was to research the potential theory for the elliptic type or the parabolic type in unbounded domains. In our study of the behavior of the solutions (harmonic functions) of the elliptic type differential equations i.e.Laplace equations in the neighbouhood of the point at infinity, we could consider qualitative properties and quantitative properties of thin sets on the complimentary sets of which the solutions behave very regularly. But the problems analogous to the solutions (temperatures) of the parabolic type differential equations i.e. heat equations could be almost unsolved except the problem about "the sets of determinations".
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Report
(4 results)
Research Products
(45 results)
