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Trudy Mat. Inst. Steklova, 2001, Volume 232, Pages 72–93 (Mi tm205)  

This article is cited in 17 scientific papers (total in 17 papers)

On the Compactness of Embeddings of Weighted Sobolev Spaces on a Domain with Irregular Boundary

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Sufficient conditions are established for the compactness of the embedding of the weighted Sobolev spaces $W_p^s$, $s\in\mathbb N$, into the weighted Lebesgue space $L_q$ for domains with irregular boundaries, in particular, for a cusp domain. The conditions imposed on the domain are formulated in simple geometrical terms (of a degenerate flexible cone).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 66–87

Bibliographic databases:
UDC: 517.51
Received in October 2000

Citation: O. V. Besov, “On the Compactness of Embeddings of Weighted Sobolev Spaces on a Domain with Irregular Boundary”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 72–93; Proc. Steklov Inst. Math., 232 (2001), 66–87

Citation in format AMSBIB
\Bibitem{Bes01}
\by O.~V.~Besov
\paper On the Compactness of Embeddings of Weighted Sobolev Spaces on a~Domain with Irregular Boundary
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 72--93
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851441}
\zmath{https://zbmath.org/?q=an:1006.46026}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 66--87


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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. O. V. Besov, “Spaces of Functions of Fractional Smoothness on an Irregular Domain”, Math. Notes, 74:2 (2003), 157–176  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    3. E. G. D'yakonov, “Strengthened Sobolev Spaces for Domains with Irregular Boundary”, Proc. Steklov Inst. Math., 243 (2003), 204–219  mathnet  mathscinet  zmath
    4. D'yakonov E.G., “On some modifications of the Steklov spectral problem for two–dimensional domains with irregular boundaries”, Dokl. Math., 67:1 (2003), 50–54  mathnet  mathscinet  zmath  zmath  isi
    5. O. V. Besov, “Function Spaces of Lizorkin–Triebel Type on an Irregular Domain”, Proc. Steklov Inst. Math., 260 (2008), 25–36  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. Besov O.V., “Spaces of functions of fractional smoothness on an irregular domain”, Dokl. Math., 79:2 (2009), 223–226  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain”, Proc. Steklov Inst. Math., 269 (2010), 25–45  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. B. V. Trushin, “Continuity of embeddings of weighted Sobolev spaces in Lebesgue spaces on anisotropically irregular domains”, Proc. Steklov Inst. Math., 269 (2010), 265–283  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russian Journal of Mathematical Physics, 18:3 (2011), 353–385  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Vasil'eva A.A., “Kolmogorov Widths of Weighted Sobolev Classes on a Domain for a Special Class of Weights. II”, Russian Journal of Mathematical Physics, 18:4 (2011), 465–504  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. Romanov A.S., “Funktsii i otobrazheniya sobolevskogo tipa na metricheskikh prostranstvakh”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 275–288  elib
    12. A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    13. Vasil'eva A.A., “Embedding Theorem for Weighted Sobolev Classes on a John Domain with Weights That Are Functions of the Distance to Some H-Set”, Russ. J. Math. Phys., 20:3 (2013), 360–373  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Vasil'eva A.A., “Embedding Theorem for Weighted Sobolev Classes with Weights That Are Functions of the Distance to Some H-Set”, Russ. J. Math. Phys., 21:1 (2014), 112–122  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Vasil'eva A.A., “Widths of Weighted Sobolev Classes on a John Domain: Strong Singularity at a Point”, Rev. Mat. Complut., 27:1 (2014), 167–212  crossref  mathscinet  zmath  isi  scopus  scopus
    16. A. A. Vasil'eva, “Widths of Sobolev weight classes on a domain with cusp”, Sb. Math., 206:10 (2015), 1375–1409  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Mueller F., Schwab Ch., “Finite elements with mesh refinement for elastic wave propagation in polygons”, Math. Meth. Appl. Sci., 39:17 (2016), 5027–5042  crossref  mathscinet  zmath  isi  scopus
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