Abstract
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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This work was partially funded by JSPS KAKENHI # 18K13441.
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Communicated by Y. Giga.
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Ioku, N. Attainability of the best Sobolev constant in a ball. Math. Ann. 375, 1–16 (2019). https://doi.org/10.1007/s00208-018-1776-7
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DOI: https://doi.org/10.1007/s00208-018-1776-7