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  • Research Article
  • Open Access

General Hardy inequalities with optimal constants and remainder terms

Journal of Inequalities and Applications20052005:628485

  • Received: 1 July 2003
  • Published:


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.

Authors’ Affiliations

School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China
Department of Mathematics, School of Science, University of Science and Technology of China, Anhui, Hefei, 230026, China


© Yaotian and Zhihui 2005