Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems

被引：61
|
作者：
Bellazzini, Jacopo [1 ]
Frank, Rupert L. [2 ]
Visciglia, Nicola [3 ]
机构：
[1] Univ Sassari, I-07100 Sassari, Italy
[2] CALTECH, Pasadena, CA 91125 USA
[3] Univ Pisa, Dipartimento Matemat, I-56100 Pisa, Italy
来源：
MATHEMATISCHE ANNALEN | 2014年 / 360卷 / 3-4期
基金：
美国国家科学基金会;
关键词：
CONCENTRATION-COMPACTNESS PRINCIPLE; SHARP CONSTANTS; EXISTENCE; SOBOLEV; EQUATIONS; CALCULUS;
D O I：
10.1007/s00208-014-1046-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo-Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb's Translation Lemma and a Riesz energy version of the Br,zis-Lieb lemma.
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页码：653 / 673
页数：21
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