| Project/Area Number |
12640212
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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 | Yamaguchi University |
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Principal Investigator |
NAKAUCHI Nobumitsu Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50180237)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAKUWA Shoichiro Tokyo Metropolitan University, Faculty of Science, Associate Professor, 理学部, 助教授 (10183435)
TAKEUCHI Hiroshi Shikoku University, Faculty of Management and Information Science, Professor, 経営情報学部, 教授 (20197271)
KAWAI Shigeo Saga University, Faculty of Culture and Education, Professor, 文化教育学部, 教授 (30186043)
NAITOH Hiroo Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (10127772)
KATO Shin Osaka City University, Faculty of Science, Associate Professor, 理学部, 助教授 (10243354)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2000: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | n-harmonic map / p-harmonic map / harmonic map / global analysis / variational problem / elliptic equation / 共形幾何構造 / Concentration phenomenon |
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| Research Abstract |
We studied n-harmonic maps and more generally p-harmonic maps for applications to the geometry of conformal structures. Nakauchi and Kawai gave some estimates for the first eigenvalue of the p-Lapalacian. We obtained an estimate of Lichnerowicz type if the Ricci curvature is bounded from below by a positive constant, and an estimate of Li-Yau type if the Ricci curvature is non-negative. In our proof of these estimates, we used Bochner-Weitzonbeck formulas of different types. The estimate of Lichnerowicz type was proved for more general class. Kawai investigated Kato type inequalities for p-harmonic maps, and got some estimates. Takakuwa studied behaviors of solution of certain nonlinear elliptic systems, and gave an estimate on the first order derivatives. He also proved uniqueness of solutions of such elliptic systems on bounded domains in the Euclidean space, using a kind of Pohozaev identity. With such supports from various spects, Nakauchi studied n-harmonic maps, and gave a relationship between n-harmonic maps and conformal Killing vector fields.
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