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Compactness of Embeddings Between Banach Spaces and Applications to Sobolev Spaces

✍ Scribed by Canavati, J. A.; Galaz-Fontes, F.


Book ID
120095930
Publisher
Oxford University Press
Year
1990
Tongue
English
Weight
308 KB
Volume
s2-41
Category
Article
ISSN
0024-6107

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Measures of non–compactness of classical
✍ Stanislav Hencl πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 221 KB

## Abstract Let Ξ© be an open subset of ℝ^__n__^ and let __p__ ∈ [1, __n__). We prove that the measure of non–compactness of the Sobolev embedding __W__^__k,p__^~0~(Ξ©) β†’ __L__^__p__\*^(Ξ©) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.