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Статья «ON THE DEFECT OF COMPACTNESS IN SOBOLEV EMBEDDINGS ON RIEMANNIAN MANIFOLDS, "Алгебра и анализ"»

Авторы:
  • TINTAREV C.1
стр. 36-54
Платно
1 Sankt Olofsgatan
  • SDI: 007.001.0234-0852.2019.031.003.3
Ключевые слова:
  • concentration compactness
  • profile decomposition
  • weak convergence
  • Sobolev spaces on manifolds
Аннотация:
The defect of compactness for an embedding E ? 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.

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