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Journal of Inequalities and Applications
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General Hardy inequalities with optimal constants and remainder terms

Journal of Inequalities and Applications volume 2005, Article number: 628485 (2005) Cite this article

Abstract

One-dimensional Hardy inequalities with weights and remainder terms are studied. The corresponding optimal constants are discussed. Then by the process of symmetrization, Hardy inequalities with remainder terms in high-dimensional Sobolev spaces are obtained. This result gives a positive answer to the Brézis-Vázquez conjecture.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China

    Shen Yaotian & Chen Zhihui

  2. Department of Mathematics, School of Science, University of Science and Technology of China, Anhui, Hefei, 230026, China

    Chen Zhihui

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  1. Shen Yaotian
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  2. Chen Zhihui
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Correspondence to Shen Yaotian.

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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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Yaotian, S., Zhihui, C. General Hardy inequalities with optimal constants and remainder terms. J Inequal Appl 2005, 628485 (2005). https://doi.org/10.1155/JIA.2005.207

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  • DOI: https://doi.org/10.1155/JIA.2005.207