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On the characterization of the compact embedding of Sobolev spaces

✍ Scribed by Bucur, Dorin; Buttazzo, Giuseppe

Book ID: 113046789
Publisher: Springer
Year: 2011
Tongue: English
Weight: 286 KB
Volume: 44
Category: Article
ISSN: 0944-2669
DOI: 10.1007/s00526-011-0441-8

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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.