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Compactness of embeddings of sobolev type on metric measure spaces

✍ Scribed by I. A. Ivanishko; V. G. Krotov

Book ID
110149638
Publisher
SP MAIK Nauka/Interperiodica
Year
2009
Tongue
English
Weight
661 KB
Volume
86
Category
Article
ISSN
0001-4346

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Measures of non–compactness of classical
Measures of non–compactness of classical embeddings of Sobolev spaces
✍ 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.