The second best constant for the Hardy-Sobolev inequality on manifolds
Analysis of PDEs
2020-06-25 v1
Abstract
We consider the second best constant in the Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with the existence of extremal functions for this inequality. This problem was tackled by Djadli-Druet [5] for Sobolev inequalities. Here, we establish the corresponding result for the singular case. In addition, we perform a blow-up analysis of solutions Hardy-Sobolev equations of minimizing type. This yields informations on the value of the second best constant in the related Riemannian functional inequality.
Keywords
Cite
@article{arxiv.2006.13371,
title = {The second best constant for the Hardy-Sobolev inequality on manifolds},
author = {Hussein Cheikh Ali},
journal= {arXiv preprint arXiv:2006.13371},
year = {2020}
}