| 含函数微分的积分不等式 |
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| 引用本文： | 吴树宏,肖加清.含函数微分的积分不等式[J].吉林大学学报(理学版),2011,49(4):652-658. |
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| 作者姓名： | 吴树宏 肖加清 |
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| 作者单位： | 武汉理工大学 理学院数学系, 武汉 430070 |
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| 基金项目： | 国家自然科学基金，中央高校基本科研业务费专项基金 |
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| 摘 要： | 利用变分方法构造并证明了含变元微分的积分不等式方法,并用该方法推广了Hilbert不等式和Opial不等式,求出了下述不等式的最优常数: ∫Ω∫ΩF(x,y)f(x) g(y) dxdy≤C∫Ωp(x)Dβ1f(x))]2dx∫Ωp(x)Dβ2g(x)]2dx]1/2, C1∫Ωp(x)Dαf(x)]2d...
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| 关 键 词： | 积分不等式 变分法 微分 |
| 收稿时间： | 2010-10-08 |
Integral Inequality Including Function Derivate |
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| WU Shu-hong,XIAO Jia-qing.Integral Inequality Including Function Derivate[J].Journal of Jilin University: Sci Ed,2011,49(4):652-658. |
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| Authors: | WU Shu-hong XIAO Jia-qing |
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| Institution: | Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China |
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| Abstract: | Variational method was used to construct the method to demonstrate integral inequality including function derivate and to generalize Hilbert inequality and Opial inequality. We obtained the optimal constant of the following inequalities. where F,p are positive definite functions. |
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| Keywords: | integral inequality variational derivate |
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