Unique continuation problems and complex phase methods in the theory of partial differential equations
| Project/Area Number |
22540185
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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 京都大学, 理学(系)研究科(研究院), 准教授 (20160426)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 解の一意接続性 / ディラック作用素 / 放物型方程式 / スペクトル問題 / 解析学 / 解析・評価 / 関数方程式論 / 数理物理学 / 函数解析 / スペクトル / コーシ-問題 / 解析接続 / 強一意接続性 / コーシー-グルサー問題 / Dirac作用素 |
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| Outline of Final Research Achievements |
We investigated spectral properties of Dirac operators for the relativistic particles like electrons and obtained important results on its essential self-adjointness and the absence of eigenvalues at the thresholds. Moreover, we established the strong unique continuation property for parabolic operators of second order with singular potentials. In addition, we revealed a global structure of the singularities of solutions to the Cauchy problem for a partial differential equation in the whole complex domain.
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Report
(6 results)
Research Products
(12 results)
