1998 Fiscal Year Final Research Report Summary
Cooperative Research on PDE
| Project/Area Number |
08045024
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | University-to-University Cooperative Research |
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| Research Field |
解析学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
OKAJI Takeshi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20160426)
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| Co-Investigator(Kenkyū-buntansha) |
DE CARLI Laura Univ of Naples, Faculty of Science, Assistant, 理学部, 助手
FERONE Vincenzo Univ of Naples, Faculty of Science, Associate Professor, 理学部, 助教授
TROMBETTI Guido Univ of Naples, Faculty of Science, Professor, 理学部, 教授
WATANABE Shinzo Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90025297)
DOI Shin-ichi Kyoto Univ., Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (00243006)
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| Project Period (FY) |
1996 – 1998
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| Keywords | Unique continuation / Smoothing effects / Schroedinger eguation / Dirac equation / Symmetrization |
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| Research Abstract |
Okaji and De Carl studied unique continuation properties for elliptic equations. First of all, Okaji investigated unique continuation properties for solutions of elliptic equations with characteristics of constant multiplicity to show that the unique continuation property holds when the multiplicity s equal to four Furthermore, two joint researches about strong unique continuation property were done by Okaji and De Carli. One of them was devoted to the study the property for the Schroedinger equations with singular potential. The other concerned the same property for the Dirac equation with singular potential.
The local structure and global structure for solutions of the Shroedinger equations were studied by Okaji and Doi. They clarified the basic structure of smoothing effects and propagation of singularities of solutions in detail by using tools in microlocal analysis.
Ferone, Trombetti, Alvino and Posteraro studied the basic structure of solutions of elliptic equations and parabolic equations by using various symmetrization methods or tools in real analysis.
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