Studies on nonlinear partial differential equations via potential analysis
| Project/Area Number |
22740081
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Hiroshima University (2013)
Akita University (2010-2012) |
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Principal Investigator |
HIRATA Kentaro 広島大学, 理学(系)研究科(研究院), 准教授 (30399795)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ポテンシャル論 / 偏微分方程式 / 実解析 / 複素解析 / 熱方程式 / 半線形楕円型方程式 / 境界挙動 / 半線形放物型方程式 / 特異点 / 熱核 / 大域的評価 / ハルナック不等式 / 除去可能集合 / ハウスドルフ次元 |
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| Research Abstract |
We have investigated, from the point of view of potential theory, some relationships among geometric properties of domains, nonlinearity of equations and properties of solutions of nonlinear partial differential equations. In nonsmooth domains, we obtained several results concerning a boundary growth estimate, a Harnack type inequality, the existence of nontangential limits, a characterization of removable sets for Holder continuous solutions of semilinear elliptic equations, a removability theorem for semilinear heat equations and a sharp global estimate of the heat kernel.
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Report
(5 results)
Research Products
(27 results)
