2010 Fiscal Year Final Research Report
Studies on blow-up analysis of critical variational problems and qualitative properties of solutions caused by blow-up
| Project/Area Number |
20540216
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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 |
Global analysis
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| Research Institution | Osaka City University |
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Principal Investigator |
TAKAHASHI Futoshi Osaka City University, 大学院・理学研究科, 教授 (10374901)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIO Masaharu 大阪市立大学, 大学院・理学研究科, 准教授 (90228156)
ATO Shin 大阪市立大学, 大学院・理学研究科, 准教授 (10243354)
SATO Tomohiko 学習院大学, 理学部, 客員研究員 (50397676)
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| Co-Investigator(Renkei-kenkyūsha) |
UZUKI Takashi 大阪大学, ・基礎工学研究科, 教授 (40114516)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 臨界型変分問題 / 爆発解析 / 解の定性的性質 / 漸近的非退化性 / 漸近的一意性 / 臨界ソボレフ指数 |
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| Research Abstract |
In this research, we studied various nonlinear elliptic equations associated with variational problem of so called "critical type". By using the intrinsic scale invariance of the equations involved, we made "blow up analysis" of non-compact solution sequences to the equations and by exploiting the explicit structure of solution set of the limit equations, we obtain various qualitative properties of blowing up solutions, such as asymptotic nondegeneracy, asymptotic uniqueness, and so on. Also we studied spectral property of blowing up solutions and obtain several results on this matter.
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