General Hardy inequalities with optimal constants and remainder terms
© Yaotian and Zhihui 2005
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.