On the best constant of Hardy–Sobolev inequalities |
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| Authors: | Adimurthi Stathis Filippas Achilles Tertikas |
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| Affiliation: | 1. TIFR Center, P.O. Box 1234, Bangalore 560012, India;2. Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece;3. Department of Mathematics, University of Crete, 71409 Heraklion, Greece;4. Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece |
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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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| Keywords: | 35J60 46E35 (26D10, 35J15) |
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