Hardy-Sobolev不等式的锐余项

Mathematical Journal of Ibaraki University Pub Date : 2005-01-01 DOI:10.5036/MJIU.37.39

Alnar Detalla, T. Horiuchi, Hiroshi Ando

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引用次数: 14

摘要

本文证明了下述类型的Hardy-Sobolev不等式中包含奇异权(logR/|x|)-2的尖余项的存在性:∫Ω|∇u(x)|2dx≥(n-2/2)2∫Ω|u(x)|2/|(x)|2dx对任意u∈W1, 20(Ω)， Ω是Rn, n>2中的有界定域，0∈Ω。这里剩余项的数量取决于R的选择。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sharp remainder terms of Hardy-Sobolev inequalities

In this paper we shall prove the existence of sharp remainder terms involving singular weight (logR/|x|)-2 for Hardy-Sobolev inequalities of the following type:∫Ω|∇u(x)|2dx≥(n-2/2)2∫Ω|u(x)|2/|(x)|2dx for any u∈W1, 20(Ω), Ω is a bounded domain in Rn, n>2, with 0∈Ω. Here the number of remainder terms depends on the choice of R.

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Mathematical Journal of Ibaraki University

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