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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'yaa, S. V. Poborchib

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 $W_p^l(\Omega)\to L_q(\Omega)$ 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.
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
\Bibitem{MazPob06}
\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}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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