ON THE DEFECT OF COMPACTNESS IN SOBOLEV EMBEDDINGS ON RIEMANNIAN MANIFOLDS

被引：0
|
作者：
Tintarev, C. [1 ]
机构：
[1] Sankt Olofsgatan 66B, Uppsala 75330, Sweden
来源：
ST PETERSBURG MATHEMATICAL JOURNAL | 2020年 / 31卷 / 03期
关键词：
Concentration compactness; profile decomposition; weak convergence; Sobolev spaces on manifolds; EXISTENCE;
D O I：
10.1090/spmj/1606
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The defect of compactness for an embedding E hooked right arrow F of two Banach spaces is the difference between a weakly convergent sequence in E and its weak limit, taken modulo terms vanishing in F. We discuss the structure of the defect of compactness for (noncompact) Sobolev embeddings on manifolds, giving a brief outline of the theory based on isometry groups, followed by a summary of recent studies of the structure of bounded sequences without invariance assumptions.
引用
收藏
页码：421 / 434
页数：14
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