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Mat. Sb., 2001, Volume 192, Number 3, Pages 3–26 (Mi msb548)  

This article is cited in 44 scientific papers (total in 44 papers)

Sobolev's embedding theorem for a domain with irregular boundary

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In Sobolev's embedding theorem, $W_p^s(G)\subset L_q(G)$ the relations between admissible smoothness parameters and integrability parameters are determined by the geometric properties of the domain $G$. In the present paper this result and the corresponding estimates of weak type are established for domains with irregular boundaries and in the case of weighted $L_p$$L_q$-spaces.

DOI: https://doi.org/10.4213/sm548

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English version:
Sbornik: Mathematics, 2001, 192:3, 323–346

Bibliographic databases:

UDC: 517.51
MSC: 46E45, 26D10
Received: 09.03.2000

Citation: O. V. Besov, “Sobolev's embedding theorem for a domain with irregular boundary”, Mat. Sb., 192:3 (2001), 3–26; Sb. Math., 192:3 (2001), 323–346

Citation in format AMSBIB
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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, “On the Compactness of Embeddings of Weighted Sobolev Spaces on a Domain with Irregular Boundary”, Proc. Steklov Inst. Math., 232 (2001), 66–87  mathnet  mathscinet  zmath
    2. D. A. Labutin, “Sharpness of Sobolev Inequalities for a Class of Irregular Domains”, Proc. Steklov Inst. Math., 232 (2001), 211–215  mathnet  mathscinet  zmath
    3. Besov O.V., “Spaces of functions of fractional smoothness on irregular domains”, Dokl. Math., 65:2 (2002), 248–253  mathnet  mathscinet  zmath  isi  elib
    4. Trushin B.V., “Embedding of Sobolev spaces in Orlicz spaces and in BMO spaces with power weights”, Dokl. Math., 68:1 (2003), 118–120  mathnet  mathscinet  zmath  isi  elib
    5. 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
    6. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    7. Boris V. Trushin, “Embedding of the Sobolev Space into the Orlicz and BMO Spaces with Power Weights”, Proc. Steklov Inst. Math., 243 (2003), 323–334  mathnet  mathscinet  zmath
    8. Rodriguez J.M., Yakubovich D.V., “A Kolmogorov-Szego-Krein type condition for weighted Sobolev spaces”, Indiana Univ. Math. J., 54:2 (2005), 575–598  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. V. G. Maz'ya, S. V. Poborchi, “Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains”, St. Petersburg Math. J., 18:4 (2007), 583–605  mathnet  crossref  mathscinet  zmath  elib
    10. Boris V. Trushin, “Embedding of Sobolev space in Orlicz space for a domain with irregular boundary”, Math. Notes, 79:5 (2006), 707–718  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. 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
    12. Boris V. Trushin, “Sobolev Embedding Theorems for a Class of Anisotropic Irregular Domains”, Proc. Steklov Inst. Math., 260 (2008), 287–309  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    13. Trushin B.V., “Sobolev embedding theorems for a class of irregular anisotropic domains”, Dokl. Math., 77:1 (2008), 64–67  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    14. 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
    15. Besov O.V., “Function spaces of Lizorkin-Triebel type on an irregular domain”, Nonlinear Anal., 70:8 (2009), 2842–2845  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. 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
    17. 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
    18. O. V. Besov, “Integral estimates for differentiable functions on irregular domains”, Sb. Math., 201:12 (2010), 1777–1790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Besov O.V., “Integral estimates for differentiable functions on irregular domains”, Doklady Mathematics, 81:1 (2010), 87–90  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    20. O. V. Besov, “Sobolev's embedding theorem for anisotropically irregular domains”, Eurasian Math. J., 2:1 (2011), 32–51  mathnet  mathscinet  zmath
    21. Vasil'eva A.A., “Kolmogorov Widths of Weighted Sobolev Classes on a Domain for a Special Class of Weights. II”, Russ. J. OF Math. Phys., 18:4 (2011), 465–504  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    22. Besov O.V., “Sobolev Embedding Theorem for Anisotropically Irregular Domains”, Doklady Mathematics, 83:3 (2011), 367–370  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russ. J. OF Math. Phys., 18:3 (2011), 353–385  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    24. Romanov A.S., “Funktsii i otobrazheniya sobolevskogo tipa na metricheskikh prostranstvakh”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 275–288  elib
    25. 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  mathscinet  elib
    26. 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
    27. 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  scopus
    28. 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  scopus
    29. 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  scopus
    30. O. V. Besov, “Embedding of Sobolev Spaces and Properties of the Domain”, Math. Notes, 96:3 (2014), 326–331  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    31. O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Dokl. Math, 90:3 (2014), 754  mathnet  crossref  mathscinet  zmath  scopus  scopus  scopus
    32. O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Proc. Steklov Inst. Math., 289 (2015), 96–103  mathnet  crossref  crossref  isi  elib
    33. A. Yu. Golovko, “Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains”, Proc. Steklov Inst. Math., 290:1 (2015), 277–287  mathnet  crossref  crossref  isi  elib  elib
    34. 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
    35. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    36. Besov O.V., “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15  mathnet  crossref  mathscinet  zmath  isi  scopus
    37. Vasil'eva A.A., “Embedding theorems for a weighted Sobolev class in the space L q,v with weights having a singularity at a point: Case v L q 1”, Russ. J. Math. Phys., 23:3 (2016), 392–424  crossref  mathscinet  zmath  isi  scopus
    38. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
    39. O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618  mathnet  crossref  crossref  mathscinet  isi  elib
    40. Berezhnoi E.I., Kocherova V.V., Perfilyev A.A., “Notes For Trudinger-Moser Inequality”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 030009  crossref  isi  scopus  scopus  scopus
    41. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    42. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”, Math. Notes, 103:3 (2018), 348–356  mathnet  crossref  crossref  isi  elib
    43. 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  mathnet  crossref  crossref  isi  elib
    44. Besov O.V., “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Dokl. Math., 99:1 (2019), 31–35  crossref  isi
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