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Algebra i Analiz, 2006, Volume 18, Issue 4, Pages 95–126 (Mi aa80)  

This article is cited in 10 scientific papers (total in 10 papers)

Research Papers

Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains

V. G. Maz'yaa, S. V. Poborchib

a Department of Mathematics, Linköping University, Linköping, Sweden
b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators $W_p^l(\Omega)\to L_q(\Omega)$ and $W_p^l(\Omega)\to C(\Omega)\cap L_\infty(\Omega)$ for a domain with an outward peak. More simple sufficient conditions are presented. Applications to the solvability of the Neumann problem for elliptic equations of order $2l$, $ l\ge1$, for a domain with peak are given. An imbedding theorem for Sobolev spaces on Hölder domains is stated.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:4, 583–605

Bibliographic databases:

MSC: 46E35
Received: 05.09.2005

Citation: V. G. Maz'ya, S. V. Poborchi, “Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains”, Algebra i Analiz, 18:4 (2006), 95–126; St. Petersburg Math. J., 18:4 (2007), 583–605

Citation in format AMSBIB
\by V.~G.~Maz'ya, S.~V.~Poborchi
\paper Imbedding theorems for Sobolev spaces on domains with peak and on H\"older domains
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 4
\pages 95--126
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 4
\pages 583--605

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    This publication is cited in the following articles:
    1. Durán R.G., López Garcia F., “Solutions of the divergence and analysis of the Stokes equations in planar Hölder-$\alpha$ domains”, Math. Models Methods Appl. Sci., 20:1 (2010), 95–120  crossref  mathscinet  zmath  isi  scopus
    2. 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
    3. O. V. Besov, “Sobolev's embedding theorem for anisotropically irregular domains”, Eurasian Math. J., 2:1 (2011), 32–51  mathnet  mathscinet  zmath
    4. Besov O.V., “Sobolev embedding theorem for anisotropically irregular domains”, Dokl. Math., 83:3 (2011), 367–370  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. 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
    6. Besov O.V., “Embedding of a Weighted Sobolev Space and Properties of the Domain”, Dokl. Math., 90:3 (2014), 754–757  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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
    8. 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
    9. 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
    10. A. A. Vasil'eva, “Estimates for the Kolmogorov widths of weighted Sobolev classes on a domain with cusp: case of weights that are functions of the distance from the boundary”, Eurasian Math. J., 8:4 (2017), 102–106  mathnet
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