On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1
On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1
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关于 p = 1 时的 Caffarelli-Kohn-Nirenberg 型不等式中的径向对称性及其破缺
DOI：
10.5036/mjiu.47.49
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
T. Horiuchi
中科院分区：
文献类型：
--
作者：
N. Chiba;T. Horiuchi
本文的主要目的是研究 p = 1 时的 Caffarelli-Kohn-Nirenberg 型不等式 (1.2)。我们表明，只要参数 j (cid:13) j 足够大，就会发生最佳常数的对称破缺。在论证中，我们有效地利用了 p = 1 的 Caffarelli-Kohn-Nirenberg 型不等式与权重的等周不等式之间的等价性。 1. 我们证明，只要参数 j (cid:13) j 足够大，就会发生对称性破缺。在论证中，我们有效地利用了 p = 1 的 CKN 型不等式与权重的等周不等式之间的等价性。
The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and isoperimetric inequalities with weights. 1. We show that symmetry breaking occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the CKN-type inequalities with p = 1 and isoperimetric inequalities with weights.