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arXiv · 0911.0948

On the best constant of Hardy-Sobolev Inequalities

Adimurthi·Stathis Filippas·Achilles Tertikas
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Abstract

We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli-Kohn-Nirenberg inequality. In three dimensions, in certain cases the sharp constant coincides with the best Sobolev constant.

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Adimurthi, Stathis Filippas, Achilles Tertikas. 2009-11-04. On the best constant of Hardy-Sobolev Inequalities. https://arxiv.org/abs/0911.0948

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