Study for Hamilton-Jacobi equations and logarithmic Sobolev inequality
| Project/Area Number |
24540165
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | University of Toyama |
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Principal Investigator |
FUJITA Yasuhiro 富山大学, 大学院理工学研究部(理学), 教授 (10209067)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHII Hitoshi 早稲田大学, 教育・総合科学学術院, 教授 (70102887)
ISHII Katsuyuki 神戸大学, 海事科学部, 教授 (40232227)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | Hamilton-Jacobi方程式 / 対数型Sobolevの不等式 / Lipschitz正則効果 / 超縮小性 / Hamilton--Jacobi方程式 / 函数の近似法 / 対数型 Sobolev の不等式 / Hamilton-Jacobi 方程式 / 解の正則化 / Harnack の不等式 / 対数型ソボレフの不等式「国際研究者交流」フランス |
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| Outline of Final Research Achievements |
Throughout this study, I wrote three papers. First, I gave a new and complete proof of Lp logarithmic Sobolev inequality by using the hypercontractivity of the solution of some Hamilton-Jacobi equation. Next, I clarified many properties of the inequality which is obtained by letting p→∞ in this Lp logarithmic Sobolev inequality. This was done by using Laplace transforms and the theory of regular variations. Finally, I investigated the set which determines the structure of solutions of Hamilton-Jacobi equations. This set plays the same role as the uniqueness set for boundary value problems.
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Report
(4 results)
Research Products
(15 results)
