Best evaluation of Sobolev inequality based on the perspective of special function theory
| Project/Area Number |
21540148
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KAMETAKA Yoshinori 大阪大学, 基礎工学研究科, 名誉教授 (00047218)
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| Co-Investigator(Renkei-kenkyūsha) |
NAGAI Atsushi 日本大学, 生産工学部, 准教授 (90304039)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ソボレフ不等式 / グリーン関数 / 再生核 / 最良定数 / 微分方程式 |
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| Research Abstract |
In the self-adjoint boundary value problem of 2M-th order (-1)^M (d/dx)^2M differential operator, best evaluation (best constant, best function) of a Sobolev inequality corresponding to clamped-free boundary condition were obtained. We also obtained the best evaluation of a Sobolev type inequality corresponding to the n-th order Hurwitz differential operators. In the Sobolev inequality of the discrete version that has proceeded in parallel with the best evaluation of the Sobolev inequality of the continuous version, we were able to compute the best constant of discrete Sobolev inequality on regular M-hedron for M=4, 6, 8, 12, 20. In addition to this result, we obtained the best evaluation of the discrete Sobolev inequality corresponding to a bending problem of a string. These are important results to become the clue in studying the future discrete Sobolev inequality.
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Report
(5 results)
Research Products
(32 results)
