The second best constant for the Hardy-Sobolev inequality on manifolds

Hussein Cheikh Ali

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arXiv · 2006.13371

The second best constant for the Hardy-Sobolev inequality on manifolds

Hussein Cheikh Ali

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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.

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Hussein Cheikh Ali. 2020-06-23. The second best constant for the Hardy-Sobolev inequality on manifolds. https://arxiv.org/abs/2006.13371

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