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Sobolev spaces on an arbitrary metric measure space: Compactness of embeddings

✍ Scribed by RomanovskiÄ, N. N.

Book ID: 120225740
Publisher: SP MAIK Nauka/Interperiodica
Year: 2013
Tongue: English
Weight: 254 KB
Volume: 54
Category: Article
ISSN: 0037-4466
DOI: 10.1134/S0037446613020171

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## Abstract Let Ω 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~(Ω) → __L__^__p__\*^(Ω) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.