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Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces
V. I. Burenkovab, T. V. Tararykovacb a V.A. Steklov Institute of Mathematics,
Russian Academy of Sciences,
42 Vavilov St,
117966 Moscow, Russia
b S.M. Nikol'skii Institute of Mathematics,
RUDN University,
6 Miklukho Maklay St,
117198 Moscow, Russia
c Cardiff School of Mathematics,
Cardiff University,
Senghennydd Road,
CF24 4AG Cardiff, United Kingdom
Аннотация:
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 $\Omega$.
Ключевые слова и фразы:
Sobolev spaces, pre-compact sets, embeddings of Sobolev spaces.
Поступила в редакцию: 01.09.2019
Образец цитирования:
V. I. Burenkov, T. V. Tararykova, “Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces”, Eurasian Math. J., 10:4 (2019), 14–23
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj344 https://www.mathnet.ru/rus/emj/v10/i4/p14
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