2011 Fiscal Year Final Research Report
Potential theoretical research for nonlinear partial differential equations
| Project/Area Number |
20540196
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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 | Fukuyama Heisei University (2010-2011)
Fukuyama University (2008-2009) |
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Principal Investigator |
ONO Takayori 福山平成大学, 福祉健康学部, 准教授 (60289270)
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| Co-Investigator(Kenkyū-buntansha) |
FUTAMURA Toshihide (90387605)
SHIMOMURA Tetsu (50294476)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 非線形偏微分方程式 / ポテンシャル論 / 優調和関数 / 除去可能集合 / 変動関数指数 / 関数空間 / ソボレフの不等式 |
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| Research Abstract |
We studied nonlinear potential theory for quasilinear partial differential equations with lower order terms. We investigated properties of superharmonic functions relative to the equation. Moreover, we characterized removable sets for continuous solutions of the equation. Also, we investigated Sobolev's inequality for functions in function spaces of variable exponent, super-polyharmonic functions and superbiharmonic functions, and boundary behavior of monotone functions in function spaces with variable exponent.
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