Missing terms in Hardy-Sobolev inequalities

Source abstract

In this article we shall investigate Hardy-Sobolev inequalities and improve them by adding a term with a singular weight of the type $(\log(1/|x|))^{-2}$. We show that this weight function is optimal in the sense that the inequality fails for any other weight more singular than this one. As an application, we use our improved inequality to study the weighted eigenvalue problem stated in §5.