Lp estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities

Abstract

Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $L^q$ regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of ${\mathbb{R}}^n$, which imply asymptotic behavior of the solutions at infinity. In addition, we find the best constant and extremals in the case of the considered $L^2$ Hardy-Sobolev inequality.

arXiv commentCorrected some typos and misprints and added a few comments and references to improve presentation. New version of Theorem 2.5 and an additional result on uniqueness/comparison principle for the considered p-laplacian equations