New developements of the regularity theory on the solutions to the Liouville-Gelfand type problems and the related parabolic dynamics
| Project/Area Number |
24654043
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Osaka City University |
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Principal Investigator |
TAKAHASHI Futoshi 大阪市立大学, 理学(系)研究科(研究院), 教授 (10374901)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIYAMA Yoshie 九州大学, 大学院・数理学研究院, 教授 (60308210)
SATO Yohei 埼玉大学, 理工学研究科, 講師 (00465387)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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 | 極解 / 非線形固有値問題 / 放物型力学系 / 特異解 / リウビル・ゲルファント型非線形固有値問題 / 半安定解 / 正則性・特異性 |
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| Research Abstract |
The aim of this research program is to solve the long open problem concerning the regularity and singularity of extremal solutions to the Liouville-Gelfand type nonlinear eigenvalue problems in a unified way, with no assumptions of the domains or the symmetry of solutions, by combining ideas from the geometric variational problems and the techniques of nonlnear analysis.
The research outputs by the research group in the period of the program, 2012-2013, are the following: 20 published papers (including accepted papers), 7 talks at Math. Soc. Japan, 21 talks by the reseach representative at seminars, including abroad.
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Report
(3 results)
Research Products
(32 results)
