2011 Fiscal Year Final Research Report
Potential theoretic study of elliptic partial differential equations
| Project/Area Number |
21540183
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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 | Hiroshima University |
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Principal Investigator |
SHIMOMURA Tetsu 広島大学, 大学院・教育学研究科, 准教授 (50294476)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUTA Yoshihiro 広島工業大学, 工学部, 教授 (00093815)
ONO Takayori 福山平成大学, 福祉健康学部, 准教授 (60289270)
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| Project Period (FY) |
2009 – 2011
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| Keywords | ソボレフ関数 / 楕円型偏微分方程式 |
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| Research Abstract |
Variable exponent Lebesgue spaces and Sobolev spaces were introduced to discuss nonlinear partial differential equations with non-standard growth condition. These spaces have attracted more and more attention in connection with the study of elasticity and electrorheological fluids. In this research, we studied the boundedness of the Hardy-Littlewood maximal operator on Orlicz-Morrey spaces with variable exponents. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolev' s inequality and Trudinger' s exponential inequality for Riesz potentials of functions in Orlicz-Morrey spaces with variable exponents.
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