Resolvent estimates for Helmholtz equations in an exterior domain and their applications to scattering problems
| Project/Area Number |
23540222
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Nippon Medical School (2012-2013)
Chiba Institute of Technology (2011) |
|---|
Principal Investigator |
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| 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 / 平滑化評価式 / 極限吸収原理 / 散乱状態の存在 / 国際研究者交流 / 国際情報交換 / 非自己共役スペクトル解析 / リゾルベント評価式 / 外部問題 / Hardy型不等式 / 弾性波動方程式 / スト-クス方程式 |
|---|
| 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.
|
Report
(4 results)
Research Products
(51 results)
