Geodesic
Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces
Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 14-23.

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Necessary and sufficient conditions on an open set $\Omega\subset \mathbb{R}^n$ are obtained ensuring that for $l,m\in\mathbb{N}_0$, $m l$ the embedding $\mathring{W}_\infty^l(\Omega)\subset W_\infty^m(\Omega)$ is compact, where $W_\infty^m(\Omega)$ is the Sobolev space and $\mathring{W}_\infty^l(\Omega)$ is the closure in $W_\infty^l(\Omega)$ of the space of all infinitely continuously differentiable functions on $\Omega$ with supports compact in $\Omega$. 
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     title = {Necessary and sufficient conditions of compactness of certain embeddings of {Sobolev} spaces},
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V. I. Burenkov; T. V. Tararykova. Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces. Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 14-23. http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a2/

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