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

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

This article is cited in 16 scientific papers (total in 16 papers)

Research Papers

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

V. G. Maz'ya^a, S. V. Poborchi^b

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

Full-text PDF (308 kB) Citations (16)

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Abstract: Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators

W_{p}^{l} (Ω) \to L_{q} (Ω)

$W_p^l(\Omega)\to L_q(\Omega)$ and

W_{p}^{l} (Ω) \to C (Ω) \cap L_{\infty} (Ω)

$W_p^l(\Omega)\to C(\Omega)\cap L_\infty(\Omega)$ 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

2 l

$2l$ ,

$l\ge1$ , for a domain with peak are given. An imbedding theorem for Sobolev spaces on Hölder domains is stated.

Received: 05.09.2005

English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 4, Pages 583–605
DOI: https://doi.org/10.1090/S1061-0022-07-00962-4

Bibliographic databases:

Document Type: Article

MSC: 46E35

Language: Russian

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

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\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

\mathnet{http://mi.mathnet.ru/aa80}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2262585}

\zmath{https://zbmath.org/?q=an:1138.46023}

\elib{https://elibrary.ru/item.asp?id=9243974}

\transl

\jour St. Petersburg Math. J.

\yr 2007

\vol 18

\issue 4

\pages 583--605

\crossref{https://doi.org/10.1090/S1061-0022-07-00962-4}

Linking options:

https://www.mathnet.ru/eng/aa80

https://www.mathnet.ru/eng/aa/v18/i4/p95

This publication is cited in the following 16 articles:

O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain in Lebesgue Spaces”, Math. Notes, 113:1 (2023), 18–26
O. V. Besov, “Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain”, Proc. Steklov Inst. Math., 323 (2023), 47–58
O. V. Besov, “Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak”, Proc. Steklov Inst. Math., 319 (2022), 43–55
Chill R., Meinlschmidt H., Rehberg J., “On the Numerical Range of Second-Order Elliptic Operators With Mixed Boundary Conditions in l-P”, J. Evol. Equ., 21:3 (2021), 3267–3288
Kukushkin M.V., “Note on the Equivalence of Special Norms on the Lebesgue Space”, Axioms, 10:2 (2021), 64
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
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
O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Proc. Steklov Inst. Math., 289 (2015), 96–103
A. A. Vasil'eva, “Widths of Sobolev weight classes on a domain with cusp”, Sb. Math., 206:10 (2015), 1375–1409
O. V. Besov, “Embedding of Sobolev Spaces and Properties of the Domain”, Math. Notes, 96:3 (2014), 326–331
Besov O.V., “Embedding of a Weighted Sobolev Space and Properties of the Domain”, Dokl. Math., 90:3 (2014), 754–757
Fedor Bakharev, Sergey Nazarov, Guido Sweers, “A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak”, Math. Mech. Compl. Sys., 1:2 (2013), 233
O. V. Besov, “Sobolev's embedding theorem for anisotropically irregular domains”, Eurasian Math. J., 2:1 (2011), 32–51
Besov O.V., “Sobolev embedding theorem for anisotropically irregular domains”, Dokl. Math., 83:3 (2011), 367–370
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
O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain”, Proc. Steklov Inst. Math., 269 (2010), 25–45

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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