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

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.

Authors’ Affiliations

(1)
School of Mathematical Sciences, South China University of Technology
(2)
Department of Mathematics, School of Science, University of Science and Technology of China

Copyright

© Yaotian and Zhihui 2005