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Mat. Sb. (N.S.), 1980, Volume 112(154), Number 1(5), Pages 56–85 (Mi msb2712)  

This article is cited in 18 scientific papers (total in 18 papers)

Imbedding theorems and compactness for spaces of Sobolev type with weights. II

P. I. Lizorkin, M. Otelbaev


Abstract: In this article theorems are established on imbedding and compactness for spaces of functions which are $p$th power summable with weight $\nu$ over the region $\Omega\subset\mathbf R^n$ and whose $m$th derivatives are $p$-summable with weight $\mu$ over $\Omega$. Moreover, necessary and sufficient conditions for the boundedness and compactness of the imbedding operator are obtained in terms of properties of the weight functions. The case of functions vanishing on the boundary is also considered. This article represents a continuation of previous research of the authors.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Sbornik, 1981, 40:1, 51–77

Bibliographic databases:

UDC: 517.518.23
MSC: 46E35
Received: 25.07.1979

Citation: P. I. Lizorkin, M. Otelbaev, “Imbedding theorems and compactness for spaces of Sobolev type with weights. II”, Mat. Sb. (N.S.), 112(154):1(5) (1980), 56–85; Math. USSR-Sb., 40:1 (1981), 51–77

Citation in format AMSBIB
\Bibitem{LizOte80}
\by P.~I.~Lizorkin, M.~Otelbaev
\paper Imbedding theorems and compactness for spaces of Sobolev type with weights.~II
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 112(154)
\issue 1(5)
\pages 56--85
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=575932}
\zmath{https://zbmath.org/?q=an:0465.46031|0447.46027}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 40
\issue 1
\pages 51--77
\crossref{https://doi.org/10.1070/SM1981v040n01ABEH001635}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MM63900003}


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    This publication is cited in the following articles:
    1. Kusainova L., Mynbaev K., “The Embedding and Compactness Theorems for Sobolev Anisotropic Weight Spaces”, 263, no. 5, 1982, 1050–1053  mathscinet  zmath  isi
    2. Pietsch A., “Eigenvalues of Integral-Operators .2.”, Math. Ann., 262:3 (1983), 343–376  crossref  mathscinet  zmath  isi
    3. Feichtinger H., “Compactness in Translation Invariant Banach-Spaces of Distributions and Compact Multipliers”, J. Math. Anal. Appl., 102:2 (1984), 289–327  crossref  mathscinet  zmath  isi
    4. Opic B., Kufner A., “Remark on Compactness of Imbeddings in Weighted Spaces”, Math. Nachr., 133 (1987), 63–70  crossref  mathscinet  zmath  isi
    5. Gurka P., Opic B., “Continuous and Compact Imbeddings of Weighted Sobolev Spaces .1.”, Czech. Math. J., 38:4 (1988), 730–744  mathscinet  zmath  isi
    6. Desiatskova N., “Theorems of Embedding and Diameters of Some Weight Classes of Smooth Functions”, 302, no. 6, 1988, 1296–1300  isi
    7. Bulabaev A., Shuster L., “On the Theory of Stourm-Liouville Difference-Equations”, 309, no. 3, 1989, 521–524  mathscinet  isi
    8. Opic B., Rakosnik J., “Estimates for Mixed Derivatives of Functions From Anisotropic Sobolev-Slobodeckij Spaces with Weights”, Q. J. Math., 42:167 (1991), 347–363  crossref  mathscinet  zmath  isi
    9. Brown R., Opic B., “Embeddings of Weighted Sobolev Spaces Into Spaces of Continuous-Functions”, Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci., 439:1906 (1992), 279–296  crossref  mathscinet  zmath  adsnasa  isi
    10. L. K. Kusainova, “Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the space $L_p(\Omega;\omega)$”, Sb. Math., 191:2 (2000), 275–290  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. S. G. Pyatkov, “Interpolation of Weighted Sobolev Spaces”, Siberian Adv. Math., 10:3 (2000), 83–132  mathnet  mathscinet  zmath  elib
    12. Kordan Ospanov, “Coercive estimates for a degenerate elliptic system of equations with spectral applications”, Applied Mathematics Letters, 2011  crossref
    13. 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  isi
    14. 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  isi
    15. 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
    16. 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  isi
    17. 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  isi
    18. 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  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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