2017 Fiscal Year Final Research Report
Potential theory on space complexity and ideal boundary
| Project/Area Number |
25287015
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
志賀 啓成 東京工業大学, 理学院, 教授 (10154189)
須川 敏幸 東北大学, 情報科学研究科, 教授 (30235858)
平田 賢太郎 広島大学, 理学(系)研究科(研究院), 准教授 (30399795)
加須栄 篤 金沢大学, 数物科学系, 教授 (40152657)
木上 淳 京都大学, 情報学研究科, 教授 (90202035)
利根川 吉廣 東京工業大学, 理学院, 教授 (80296748)
島内 宏和 山梨英和大学, 人間文化学部, 助教 (90759200)
濱田 英隆 九州産業大学, 工学部, 教授 (30198808)
濱野 佐知子 大阪市立大学, 大学院理学研究科, 准教授 (10469588)
松村 慎一 鹿児島大学, 理工学研究科, 助教 (90647041)
川上 裕 山口大学, 理工学研究科, 講師 (60532356)
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| Co-Investigator(Renkei-kenkyūsha) |
KUMAGAI TAKASHI 京都大学, 数理解析研究所, 教授 (90234509)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | ポテンシャル / 調和 / 容量 / Green核 / 熱核 / Harnack原理 / ネットワーク / フラクタル |
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| Outline of Final Research Achievements |
Relationships among harmonic functions, solutions to the heat equation, the Green and heat kernels and their defining domains, the influence of the space complexity to the boundary behavior were studied. They were applied to various fields such as non-smooth Euclidean domains, manifolds, varifolds, networks and fractals. In particular, new results were obtained in Harnack principle with exceptional sets, estimates of the principal frequency in terms of capacitary width, sufficient conditions for the global boundary Harnack principle based on the capacitary width of sublevel sets of the Green function, conditions for the parabolic boundary Harnack principle (Intrinsic Ultracontractivity), the critical exponent of a graph domain enjoying the global boundary Harnack principle, and the 0-1 law of the capacity density at infinity and so on.
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| Free Research Field |
基礎解析学
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