Best evaluation of the Sobolev inequality using the reproducing kernel theory and its applications
| Project/Area Number |
25400210
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
亀高 惟倫 大阪大学, その他部局等, 名誉教授 (00047218)
楳田 登美男 兵庫県立大学, 物質理学研究科, 教授 (20160319)
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| Co-Investigator(Renkei-kenkyūsha) |
NAGAI Atsushi 日本大学, 生産工学部, 教授 (90304039)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ソボレフ不等式 / 最良定数 / グリーン行列 / 再生核 / グリーン関数 |
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| Outline of Final Research Achievements |
The subject of this research is to obtain best evaluation of a Sobolev inequality. In continuous version, we have treated of Thomson cable (a continuous model) and a free boundary value problem for a 2M-th order operator (no lower terms). In discrete version, we have treated the Mobius ladder, C60 fullerene buckyball, the truncated regular M-hedron (M=4,6,8) and the Toeplitz graph. In each case, we have computed a best constant and family of best functions for the Sobolev inequality. These are important results to become the clue in studying the future Sobolev inequality.
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Report
(5 results)
Research Products
(10 results)
