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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 319, Pages 51–63
DOI: https://doi.org/10.4213/tm4280 (Mi tm4280) 		 
Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak

O. V. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4280
Abstract: For a domain $G\subset \mathbb R^n$ with an anisotropic peak, we construct integral representations of functions in terms of derivatives and establish conditions for the embedding $W_p^s(G)\subset L_q(G)$ of the Sobolev space in the Lebesgue space for $1\leq p<q\le \infty $.
Keywords: Sobolev space, domain with a peak, embedding theorem.
Received: January 17, 2022
Revised: May 22, 2022
Accepted: May 30, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 319, Pages 43–55
DOI: https://doi.org/10.1134/S0081543822050042
Bibliographic databases:
Document Type: Article
UDC: 517.518.232
Language: Russian
Citation: O. V. Besov, “Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 51–63; Proc. Steklov Inst. Math., 319 (2022), 43–55
Citation in format AMSBIB
\Bibitem{Bes22}
\by O.~V.~Besov
\paper Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 51--63
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4280}
\crossref{https://doi.org/10.4213/tm4280}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 43--55
\crossref{https://doi.org/10.1134/S0081543822050042}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148466679}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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