2005 Fiscal Year Final Research Report Summary
Potential Analysis for Sobolev functions
| Project/Area Number |
14340046
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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 Sciences, Professor, 総合科学部, 教授 (00093815)
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| Co-Investigator(Kenkyū-buntansha) |
SHIBATA Tetsutaro HIROSHIMA UNIVERSITY, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (90216010)
USMAI Hiroyuki HIROSHIMA UNIVERSITY, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (90192509)
SHIMOMURA Tetsu HIROSHIMA UNIVERSITY, Graduate School of Education, Associate Professor, 大学院・教育学研究科, 助教授 (50294476)
SUZUKI Noriaki Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理学研究科, 助教授 (50154563)
MASAOKA Hiroaki Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (30219315)
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| Project Period (FY) |
2002 – 2005
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| Keywords | potential / partial differential equation / polyharmonic functions / monotone functions in the sense of Lebesgue / tangential boundary limits / function space / Sobolev's theorem / variable exponent |
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| Research Abstract |
・The head Investigator, with the help of T. Shimomura, extended the Fatou theorem for Sobolev's monotone functions in the sense of Lebesgue. In relation with Liouville's theorem and Bocher's theorem for harmonic functions, he investigated isolated singularities for polyharmonic functions. Furthermore, he studied Sobolev's function spaces with variable exponent, and extended Sobolev's theorem in the metric space setting.
・T.Shibata studied eigen value problem for elliptic partial differential equations.
・H.Usami characterized asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations
・T.Nagai treated qualitative properties of solutions to a reaction-diffusion equation with advection modelling chemotaxis.
・M.Shiba and M.Masumoto studied circularizable domains on Riemann surfaces.
・N.Suzuki and M.Nishio extended Bergman space theory for fractional heat equations.
・H.Masaoka showed a condition for the existence of positive harmonic functions with finite Dirichlet integral on Riemann surfaces.
・T.Shima and M.Furushima studied analytic compactifications in Fano manifolds.
・H.Yoshida investigated the behavior of harmonic functions on cones through minimally thin sets.
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Research Products
(12 results)
