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The measure of noncompactness of Sobolev embeddings

✍ Scribed by Nina A. Yerzakova

Publisher: SP Birkhäuser Verlag Basel
Year: 1994
Tongue: English
Weight: 409 KB
Volume: 19
Category: Article
ISSN: 0378-620X
DOI: 10.1007/bf01203670

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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.