Geodesic
On the defect of compactness in Sobolev embeddings on Riemannian manifolds
Algebra i analiz, Tome 31 (2019) no. 3, pp. 36-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: concentration compactness, profile decomposition, weak convergence, Sobolev spaces on manifolds. 
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C. Tintarev. On the defect of compactness in Sobolev embeddings on Riemannian manifolds. Algebra i analiz, Tome 31 (2019) no. 3, pp. 36-54. http://geodesic.mathdoc.fr/item/AA_2019_31_3_a2/

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