1999 Fiscal Year Final Research Report Summary
Potential the Oretic study on quasi-regular mappings
| Project/Area Number |
10440049
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Hiroshima University |
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Principal Investigator |
MIZUTA Yoshihiro Hiroshima University, Faculty of Integrated Arts and Science, Professor, 総合科学部, 教授 (00093815)
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| Co-Investigator(Kenkyū-buntansha) |
FURUSHIMA Mikio Hiroshima University, Faculty of Integrated Arts and Science, Professor, 総合科学部, 教授 (00165482)
YOSHIDA Kiyoshi Hiroshima University, Faculty of Integrated Arts and Science, Professor, 総合科学部, 教授 (80033893)
SHIMOMURA Tetsu Asahi National College of Technology, Lecturer, 講師 (50294476)
AIKAWA Hiroaki Shimane University, Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (20137889)
SHIBATA Tetsutaro Hiroshima University, Faculty of Integrated Arts and Science, Associate Professor, 総合科学部, 助教授 (90216010)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Potential theory / Complex analysis / quasi-conformal mappings / Elliptic partical differential equations / boundary behaviors |
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| Research Abstract |
The aim of this study is to investigate boundary behaviors of quasi-conformal mappings, and then apply our methods to the Dirichlet problem for non-linear elliptic equations.
In order to complete the present study, we called some meetings with investigators and discussed each other. With the help of this Grant-in-aid for Scientific Research, we successfully had the conferences on potential theory in Suuri-kaiseki-kenkyusyo, Kyoto Sangyo-University, Gifu University and Hiroshima University. Especially, in Hiroshima University, we held the workshop on real and complex analysis with famous Korean mathematicians, whose proceedings will be published soon and will be served as the further development of this study.
The Head investigator of this study was invited to the international conferences to present and give a talk. We had the great success in collecting new aspects of this study by the discussions with many famous mathematicians in the world.
Each coordinate of quasi-regular mappings are called monotone. It is very useful for us to study monotone functions in general settings, We have obtained interesting results on the boundary behaviors for monotone Sobolev functions in the unit ball. Our results will be widely delivered in some papers.
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