Missing terms in Hardy-Sobolev inequalities
Missing terms in Hardy-Sobolev inequalities
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DOI：
10.3792/pjaa.80.160
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发表时间：
2004-10
期刊：
影响因子：
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通讯作者：
Alnar Detalla;T. Horiuchi;Hiroshi Ando
中科院分区：
文献类型：
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作者：
Alnar Detalla;T. Horiuchi;Hiroshi Ando
本文将研究Hardy-Sobolev不等式，并通过增加一个具有（log（1/x））-2型奇异权的项来改进它们.我们表明，这个权重函数是最优的意义上，不等式失败的任何其他重量比这一个更奇异。作为应用，我们利用改进的不等式研究了B5中的加权特征值问题.
In this article we shall investigate Hardy-Sobolev inequalities and improve them by adding a term with a singular weight of the type (log(1/‖x‖)) - 2 . We show that this weight function is optimal in the sense that the inequality fails for any other weight more singular than this one. As an application, we use our improved inequality to study the weighted eigenvalue problem stated in Β5.