Studies on nonlinear partial differential equations by potential analysis
| Project/Area Number |
19740062
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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 | Akita University |
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Principal Investigator |
HIRATA Kentaro Akita University, 教育文化学部, 講師 (30399795)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,860,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 実解析 / 関数方程式 / 優調和関数 / 境界挙動 / 半線形楕円型方程式 / Helmholtz方程式 / 調和測度 / John領域 / Green関数 / p-Laplace方程式 / 一様領域 / 準一様領域 / Martin核 / 境界増大度 / 非線形楕円型方程式 |
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| Research Abstract |
In a bounded smooth domain, we established a suitable boundary growth estimate for positive superharmonic functions satisfying a nonlinear inequality. Moreover, we proved the existence of positive solutions of semilinear elliptic equations that are comparable to the Poisson kernel. Also, we gave a sufficient condition for Dirichlet boundary data to guarantee the existence of positive solutions of singular semilinear elliptic equations. In regard to potential theory, we studied a doubling property of harmonic measure, an estimate for the product of the Green function and the Martin kernel, and the boundary behavior of Martin kernels.
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Report
(4 results)
Research Products
(39 results)
