Attainability of the best Sobolev constant in a ball
Attainability of the best Sobolev constant in a ball
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DOI：
10.1007/s00208-018-1776-7
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发表时间：
2018-06
影响因子：
1.4
通讯作者：
Norisuke Ioku
中科院分区：
文献类型：
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作者：
Norisuke Ioku
Sobolev不等式在整个空间中的最佳常数由Aubin-Talenti函数获得;然而，由于扩张不变性的破坏，这不会发生在有界区域中。本文研究了球上Sobolev不等式的一种新的尺度不变形式，并证明了它的最佳常数是由Aubin-Talenti型函数得到的.本文还讨论了球上Caffarelli-Kohn-Nirenberg不等式的推广。
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.