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Sibirsk. Mat. Zh., 2014, Volume 55, Number 3, Pages 627–649 (Mi smj2559)  

This article is cited in 1 scientific paper (total in 1 paper)

Embedding theorems and a variational problem for functions on a metric measure space

N. N. Romanovskiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We use a new method to prove the Sobolev embedding theorem for functions on a metric space and study other questions of the theory of Sobolev spaces on a metric space. We prove the existence and uniqueness of solution to a variational problem.

Keywords: Sobolev classes, Nikol'skiĭ classes, functions on a metric space, embedding theorems, compactness of the embedding, variational problem.

Full text: PDF file (430 kB)
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English version:
Siberian Mathematical Journal, 2014, 55:3, 511–529

Bibliographic databases:

UDC: 517.518+517.518.23
Received: 06.08.2013

Citation: N. N. Romanovskiǐ, “Embedding theorems and a variational problem for functions on a metric measure space”, Sibirsk. Mat. Zh., 55:3 (2014), 627–649; Siberian Math. J., 55:3 (2014), 511–529

Citation in format AMSBIB
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\by N.~N.~Romanovski{\v\i}
\paper Embedding theorems and a~variational problem for functions on a~metric measure space
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 3
\pages 627--649
\mathnet{http://mi.mathnet.ru/smj2559}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237379}
\elib{http://elibrary.ru/item.asp?id=21800679}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 3
\pages 511--529
\crossref{https://doi.org/10.1134/S0037446614030136}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000338502400013}
\elib{http://elibrary.ru/item.asp?id=24061968}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903316780}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. N. Romanovskiǐ, “Sobolev embedding theorems and generalizations for functions on a metric measure space”, Siberian Math. J., 59:1 (2018), 126–135  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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