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arXiv · 1807.00127

Attainability of the best Sobolev constant in a ball

Norisuke Ioku
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Abstract

The best constant of the Sobolev inequality in the whole space is attained by the Aubin-Talenti function; however, this does not happen in bounded domains because the break in 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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Norisuke Ioku. 2018-06-30. Attainability of the best Sobolev constant in a ball. https://arxiv.org/abs/1807.00127

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