Compactness via symmetrization

被引：29
作者：
Burchard, A [1 ]
Guo, Y
机构：
[1] Univ Virginia, Dept Math, Charlottesville, VA 22902 USA
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 214卷 / 01期
基金：
美国国家科学基金会;
关键词：
symmetric rearrangement; concentration compactness; dynamical stability; Hardy-Littlewood-Sobolev inequality; Sobolev inequality; Euler-Poisson system; Vlasov-Poisson system; stellar dynamics;
D O I：
10.1016/j.jfa.2004.04.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider two types of translation-invariant functionals I and J on R-m, and a sequence of functions f(n), whose corresponding symmetric rearrangements f(n)* are convergent. We show that f(n) themselves converge up to translations if either lim(n-->proportional to) I (f(n))= lim(n-->infinity)(f(n)*) or lim(n-->infinity) J (f(n)) = lim(n-->infinity)J(f(n)*). These compactness results lead to applications in variational problems and stability problems in stellar dynamics. (C) 2004 Elsevier Inc. All rights reserved.
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收藏
页码：40 / 73
页数：34
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