On the defect of compactness in Sobolev embeddings on Riemannian manifolds
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- by C. Tintarev
- St. Petersburg Math. J. 31 (2020), 421-434
- DOI: https://doi.org/10.1090/spmj/1606
- Published electronically: April 30, 2020
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Abstract:
The defect of compactness for an embedding $E\hookrightarrow F$ 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.References
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Bibliographic Information
- C. Tintarev
- Affiliation: Sankt Olofsgatan 66B, 75330 Uppsala, Sweden
- MR Author ID: 172775
- ORCID: 0000-0002-7484-2900
- Email: tammouz@gmail.com
- Received by editor(s): August 30, 2018
- Published electronically: April 30, 2020
- © Copyright 2020 American Mathematical Society
- Journal: St. Petersburg Math. J. 31 (2020), 421-434
- MSC (2010): Primary 46E35, 46B50, 46N20, 54D30, 43A99, 58E99
- DOI: https://doi.org/10.1090/spmj/1606
- MathSciNet review: 3985919
Dedicated: Dedicated to the memory of S. G. Mikhlin