Open Access

General Hardy inequalities with optimal constants and remainder terms

Journal of Inequalities and Applications20052005:628485

DOI: 10.1155/JIA.2005.207

Received: 1 July 2003

Published: 11 July 2005


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
Department of Mathematics, School of Science, University of Science and Technology of China


© Yaotian and Zhihui 2005