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Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms

Abstract

We consider a class of sharp Hardy-Sobolev inequality, where the weights are functions of the distance from a surface. It is proved that the Hardy-Sobolev inequality can be successively improved by adding to the right-hand side a lower-order term with optimal weight and constant.

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Correspondence to Zhihui Chen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Shen, Y., Chen, Z. Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms. J Inequal Appl 2009, 419845 (2009). https://doi.org/10.1155/2009/419845

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Keywords

  • Optimal Weight
  • Full Article
  • Remainder Term
  • General Weight
  • Publisher Note