2013 Fiscal Year Final Research Report
Resolvent estimates for Helmholtz equations in an exterior domain and their applications to scattering problems
| Project/Area Number |
23540222
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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 | Nippon Medical School (2012-2013)
Chiba Institute of Technology (2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KADOWAKI Mitsuteru 愛媛大学, 大学院・理工学研究科, 准教授 (70300548)
WATANABE Kazuo 学習院大学, 理学部, 助教 (90260851)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 偏微分方程式論 / 数学的散乱理論 / スペクトル解析 / リゾルベント評価 / 極限吸収の原理 / 極限振幅の原理 |
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| Research Abstract |
We studied the Helmholtz equation, which is appeared in classical physics as wave equations, and in quantum mechanics as Schr\"odinger equations. We established the uniform resolvent estimate including the case of a two-dimensional, which is important in the scattering problem, corresponding as the application. In particular, in 2-D case, we find that we can compensate the term which remain negative term using the Hardy type inequalities related to radiation conditions. As a result, we can prove the uniform resolvent estimate in 2D case, which was already proved in $N(\geqq3)$ D case.
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