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

页码：421 / 434

页数：14

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