# Attainability of the best Sobolev constant in a ball

@article{Ioku2018AttainabilityOT, title={Attainability of the best Sobolev constant in a ball}, author={Norisuke Ioku}, journal={Mathematische Annalen}, year={2018}, pages={1-16} }

The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.

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