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Eurasian Mathematical Journal, 2011, Volume 2, Number 1, Pages 81–103 (Mi emj43)  
This article is cited in 2 scientific papers (total in 2 papers)

A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant

G. A. Chechkinab, Yu. O. Korolevaac, L.-E. Perssonc, P. Wallc

a Department of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Narvik University College, Narvik, Norway
c Department of Mathematics, Luleå University of Technology, Luleå, Sweden
Full-text PDF (386 kB) Citations (2)
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Abstract: We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space $H^1$ having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.
Keywords and phrases: partial differential equations, functional analysis, spectral theory, homogenization theory, Hardy-type inequalities, Friedrichs-type inequalities.
Received: 11.10.2010
Bibliographic databases:
Document Type: Article
MSC: 35B27, 39A10, 39A11, 39A70, 39B62, 41A44, 45A05
Language: English
Citation: G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall, “A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant”, Eurasian Math. J., 2:1 (2011), 81–103
Citation in format AMSBIB
\Bibitem{CheKorPer11}
\by G.~A.~Chechkin, Yu.~O.~Koroleva, L.-E.~Persson, P.~Wall
\paper A new weighted Friedrichs-type inequality for a~perforated domain with a~sharp constant
\jour Eurasian Math. J.
\yr 2011
\vol 2
\issue 1
\pages 81--103
\mathnet{http://mi.mathnet.ru/emj43}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2910822}
\zmath{https://zbmath.org/?q=an:1234.35027}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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