Variational approach to elliptic partial differential equations associated with critical functional inequalities
| Project/Area Number |
16K21056
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
Mathematical analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 臨界関数不等式 / 楕円型不等式 / 変分解析 / 楕円型方程式 / 関数不等式 / 有界変動関数 / Trudinger-Moser不等式 / Trudinger-Moser型不等式 / 臨界型関数不等式 / 変分問題 / Moser-Trudinger不等式 / 実関数論 / 関数方程式論 |
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| Outline of Final Research Achievements |
(1)One of applicant's main research is (*) to establish several functional inequalities concerning Sobolev's embedding theorem, and (**) to investigate the solutions of Euler-Lagrange equations (elliptic partial differential equations) associated with functional inequalities. (2)Another one is to re-consider the relations between themes (*) and (**), and to give a systematic approach for those themes (*) and (**). As a result, applicant succeeded in publishing several academic papers related on the themes (1) and (2).
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| Academic Significance and Societal Importance of the Research Achievements |
応募者の主な研究テーマはソボレフ空間上の種々の臨界不等式、または同不等式からEuler-Lagrange方程式を介して得られる楕円型方程式の可解性を論じることである。一般に、ソボレフ空間は関数空間、関数解析および物理的応用という観点における基礎的な空間であり、同空間の諸性質の精緻な解析は、数学的および物理的な応用という意味において多くの効果が期待される。
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Report
(5 results)
Research Products
(17 results)
