| Project/Area Number |
15K04962
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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 |
Mathematical analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
Masashi Misawa 熊本大学, 大学院先端科学研究部(理), 教授 (40242672)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAURA Yoshihiko 日本大学, 文理学部, 教授 (90255597)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 偏微分方程式 / 退化特異放物型方程式系 / 正則性特異性 / 調和写像 / 調和写像熱流 / p調和写像 / p調和写像熱流 / p調和方程式 / 退化特異楕円型 / p調和写像流 / 退化特異放物型 |
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| Outline of Final Research Achievements |
The p-harmonic flow is the heat flow for the p-harmonic maps,the critical
points for p-energy for maps beteween two smooth compact Riemannian manifolds, and given by the degenerate and singular parabolic system of 2nd ordered partial differential equations of so-called p-Laplcian type. We study the regularity and singularity of solutions of the p-harmonic flows. Our main result is the local regularity theorem, which holds true uniformly for the p-energy bounded, regular solutions of the p-harmonic flows. Based on this local regularity theorem, we prove that the weak limits of p-energy bounded, regular p-harmonic flows are partial regular weak solutions of the p-harmonic flows, with the almost optimal size estimation by Hausdorff measure, of their singular sets, the exceptional sets of regularity.
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