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Caffarelli-Kohn-Nirenberg不等式的证明 被引量：2

Proof of Caffarelli-Kohn-Nirenberg inequality
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摘要 先用函数表示和Picone恒等式的方法建立高维欧氏空间的一类Hardy型不等式,结合CAFFARELLI、KOHN、NIRENBERG三人证明Caffarelli-Kohn-Nirenberg不等式的思想,给出Caffarelli-Kohn-Nirenberg不等式的证明,突破原文需转化为一维情形的限制,对高维空间的情形直接证明,易于推广. A class of Hardy type inequality is given by the method of function representation and the method of Picone indentity on R^n. With the idea of Caffarelli, Kohn and Nirenberg to prove Caffarelli-Kohn-Nirenberg inequality, the new proof for the inequality is given. This new method can be applied on the space with any dimension and generalized easily.
作者 韩亚洲 张书陶
机构地区 中国计量学院数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2007年第5期492-498,共7页 Journal of Zhejiang University（Science Edition）
基金 浙江省自然科学基金资助项目(Y606144) 中国计量学院校立项目"Heisenberg群的Liouville性质"
关键词 Caffarelli-Kohn-Nirenberg不等式 HARDY型不等式 函数表示 PICONE恒等式 Caffarelli-Kohn-Nirenberg inequality Hardy type inequality function representation Picone identity
分类号 O178 [理学—基础数学]
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参考文献10

  • 1CAFFARELLI L,KOHN R,NIRENBERG L.First order interpolation inequalities with weights[J].Compositio Mathematica,1984,53:259-275.
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二级参考文献10

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浙江大学学报（理学版）
2007年 第5期

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