2009 Fiscal Year Final Research Report
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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| Keywords | 実解析 / 関数方程式 |
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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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