Strong unique continuation property and limiting absorption principle for partial differential systems with their applications
| Project/Area Number |
18540173
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
TAKASHI Okaji (OKAJI Takashi) Kyoto University, 大学院・理学研究科, 准教授 (20160426)
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| Co-Investigator(Kenkyū-buntansha) |
山田 修宣 立命館大学, 理工学部, 教授 (70066744)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Osanobu 立命館大学, 理工学部, 教授 (70066744)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,120,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 偏微分方程式系 / 解の一意接続性 / 極限吸収原理 / ディラック作用素 / ストークス方程式 / 強-意接続性 / スペクトル / 相対論的シュレディンガー作用素 / 強一意接続性 |
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| Research Abstract |
We investigate properties of solutions to system of equations including the Dirac equation which described the relativistic particles like electrons. In particular we establish that the Dirac equation with potential homogeneous of degree zero has only absolutely continuous spectra and it has no bound states if the velocity of light is large enough. Moreover we prove that the Stokes equation in fluid mechanics has strong unique continuation property even if its coefficients have strong singularities with critical order.
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Report
(6 results)
Research Products
(15 results)
