TY - JOUR
T1 - Attainability of the best Sobolev constant in a ball
AU - Ioku, Norisuke
N1 - Funding Information:
This work was partially funded by JSPS KAKENHI # 18K13441.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/10/8
Y1 - 2019/10/8
N2 - 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.
AB - 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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U2 - 10.1007/s00208-018-1776-7
DO - 10.1007/s00208-018-1776-7
M3 - Article
AN - SCOPUS:85056664135
VL - 375
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1-2
ER -