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

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

2006-01-27

arxiv.org/abs/math/0601662v3

Mathematics

Analysis of PDEs

Corrected some typos and misprints and added a few comments and references to improve presentation. New version of Theorem 2.5

Scientific paper

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.

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