Symmetry of solutions for elliptic partial differential equations
| Project/Area Number |
24540179
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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 |
Basic analysis
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| Research Institution | Saga University |
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Principal Investigator |
Kajikiya Ryuji 佐賀大学, 工学(系)研究科(研究院), 教授 (10183261)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 楕円型偏微分方程式 / 変分法 / 最小エネルギー解 / 解の対称性 / 群不変性 / 劣線形熱方程式 / 定常解の安定性 / 準線形放物型偏微分方程式 / p-Laplace方程式 / 非線形ノイマン問題 / 分岐 / p-Laplace 方程式 / least energy solution / elliptic equation |
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| Outline of Final Research Achievements |
We study elliptic partial differential equations in symmetric domains. Let H and G be closed subgroups of the orthogonal group such that H is a closed subgroup of G and the domain is G invariant. Then we show the existence of a positive solution which is H invariant but G non-invariant under suitable assumptions of H, G and the coefficient function of the equation. Such a solution is obtained as a least energy solution. Here a least energy solution is a solution which is a minimizer of the Rayleigh quotient. Our theorem ensures the existence of various solutions which has a weak symmetry but does not have a strong symmetry.
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Report
(5 results)
Research Products
(51 results)
