On the best constant of Hardy-Sobolev Inequalities
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constantinequalitybesthardy-sobolevsharpcaffarelli-kohn-nirenbergcasescertain
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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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