2011 Fiscal Year Final Research Report
On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equations
| Project/Area Number |
20540153
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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 |
Basic analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
ONISHI Kazuei 茨城大学, 理学部, 教授 (20078554)
SHIMOMURA Katunori 茨城大学, 理学部, 教授 (00201559)
NAKAI Eiichi 茨城大学, 理学部, 教授 (60259900)
ANDO Hiroshi 茨城大学, 理学部, 講師 (60292471)
YAMAGAMI Shigeru 茨城大学, 理学部, 教授 (90175654)
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| Co-Investigator(Renkei-kenkyūsha) |
HOSHIRO Toshihiko 兵庫県立大学, 教授 (40211544)
TACHIZAWA Kazuya 北海道大学, 理学研究科, 教授 (80227090)
SATO Tokushi 東北大学, 理学研究科, 助教 (00261545)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 重み付きソボレ不等式 / 重み付きハーディ不等式 / CKN型不等式 / ミッシング・ターム / 退化楕円型方程式 / 非線形変分問題 |
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| Research Abstract |
(1) The classical Hardy-Sobolev inequalities were improved by finding out sharp missing terms and the best constants.(2) By making effective use of the improved Hardy-Sobolev inequalities, nonlinear problems were successfully studied.(3) By a linearization method the symmetry breaking of the Caffarelli-Khon-Nirenberg type inequalities were investigated to make clear its mechanism.(4) The operators on the Orlicz with a variable exponent p(x) were studied using the Hardy inequalities.
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