Abstract:
We establish the embedding Wsp,v(G)⊂Lq,w(G) for a weighted Sobolev space defined on an irregular domain G in the case of the limiting exponent when the parameters satisfy certain relations that depend on the geometric properties of the domain G.
Citation:
O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 107–114; Proc. Steklov Inst. Math., 289 (2015), 96–103
\Bibitem{Bes15}
\by O.~V.~Besov
\paper Embedding of a weighted Sobolev space and properties of the domain
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 107--114
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3630}
\crossref{https://doi.org/10.1134/S0371968515020065}
\elib{https://elibrary.ru/item.asp?id=23738464}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 289
\pages 96--103
\crossref{https://doi.org/10.1134/S0081543815040069}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000358577300006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938895219}
Linking options:
https://www.mathnet.ru/eng/tm3630
https://doi.org/10.1134/S0371968515020065
https://www.mathnet.ru/eng/tm/v289/p107
This publication is cited in the following 6 articles:
O. V. Besov, “Embeddings for weighted spaces of functions of positive smoothness on irregular domains into Lebesgue spaces”, Dokl. Math., 97:3 (2018), 236–239
O. V. Besov, “Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space”, Math. Notes, 104:6 (2018), 799–809
O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618
O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15
O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66
Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687
Citation in format AMSBIB
Contact us: