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Mat. Zametki, 2006, Volume 79, Issue 5, Pages 767–778 (Mi mz2748)  

This article is cited in 5 scientific papers (total in 5 papers)

Embedding of Sobolev space in Orlicz space for a domain with irregular boundary

Boris V. Trushin

Moscow Institute of Physics and Technology

Abstract: In this paper, we establish the embedding of a weighted Sobolev space in an Orlicz space for a domain with irregular boundary. We find an estimate of the order of growth of the $N$-function (defining the Orlicz space) and show that, under certain additional constraints on the weights, this estimate is sharp. We also establish the embedding in the space of continuous functions.

DOI: https://doi.org/10.4213/mzm2748

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English version:
Mathematical Notes, 2006, 79:5, 707–718

Bibliographic databases:

UDC: 517.518.232
Received: 16.05.2002

Citation: Boris V. Trushin, “Embedding of Sobolev space in Orlicz space for a domain with irregular boundary”, Mat. Zametki, 79:5 (2006), 767–778; Math. Notes, 79:5 (2006), 707–718

Citation in format AMSBIB
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\by Boris~V.~Trushin
\paper Embedding of Sobolev space in Orlicz space for a~domain with irregular boundary
\jour Mat. Zametki
\yr 2006
\vol 79
\issue 5
\pages 767--778
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\transl
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\vol 79
\issue 5
\pages 707--718
\crossref{https://doi.org/10.1007/s11006-006-0080-0}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Isangulova, S. K. Vodopyanov, “Coercive estimates and integral representation formulas on Carnot groups”, Eurasian Math. J., 1:3 (2010), 58–96  mathnet  mathscinet  zmath
    2. Trushin B.V., “Vlozhenie vesovykh prostranstv soboleva v vesovye prostranstva orlicha i v prostranstvo nepreryvnykh funktsii na anizotropno neregulyarnykh oblastyakh”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 183–194  elib
    3. N. N. Romanovskiǐ, “Embedding theorems and a variational problem for functions on a metric measure space”, Siberian Math. J., 55:3 (2014), 511–529  mathnet  crossref  mathscinet  isi  elib  elib
    4. Harjulehto P., Hurri-Syrjanen R., Kapulainen J., “An Embedding Into An Orlicz Space For Irregular John Domains”, Comput. Methods Funct. Theory, 14:2-3, SI (2014), 257–277  crossref  mathscinet  zmath  isi  scopus
    5. Harjulehto P., Hurri-Syrjaenen R., “An Embedding into an Orlicz space for ??-Functions from Irregular Domains”, Complex Analysis and Dynamical Systems VI, Contemporary Mathematics, 653, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Khavinson D., Reich S., Weinstein G., Zalcman L., Amer Mathematical Soc, 2015, 177–189  crossref  mathscinet  zmath  isi
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