2016 Fiscal Year Final Research Report
Theory and application of divergence form elliptic operators
| Project/Area Number |
23540225
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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 | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2017-03-31
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| Keywords | elliptic operator / regularity theorem / Sobolev space / Hoelder-Zygmund space / Dirichlet condition / eigenfunction / asymptotic behavior |
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| Outline of Final Research Achievements |
This research is concerned with strongly ellptic operators in divergence or non-divergence form under Dirichlet boundary conditions. We showed that the operators are isomorphisms between suitable two Lp Sobolev spaces. Compared with previous studies, this research obtained the same conclusion under much weaker assumptions. As a corollary, we derived a regularity theorem for elliptic equations, which states that the solutions become smoother as the coefficients and the boundary of the domain become smoother. A similar result was also shown in the framework of the Hoelder spaces, which are related to classical differentiability.
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| Free Research Field |
偏微分方程式論
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