| 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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| 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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