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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 385, Pages 224–233 (Mi znsl3907)  

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

Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient

M. Fuchsa, S. Repinb

a Universität des Saarlandes, Fachbereich 6.1 Mathematik, Saarbrücken, Germany
b St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
References:
Abstract: If $\Omega\subset\mathbb R^n$ is a bounded Lipschitz domain, we prove the inequality $\|u\|_1\le c(n)\operatorname{diam}(\Omega)\int_\Omega|\varepsilon^D(u)|$ being valid for functions of bounded deformation vanishing on $\partial\Omega$. Here $\varepsilon^D(u)$ denotes the deviatoric part of the symmetric gradient and $\int_\Omega|\varepsilon^D(u)|$ stands for the total variation of the tensor-valued measure $\varepsilon^D(u)$. Further results concern possible extensions of this Poincaré-type inequality. Bibl. 27 titles.
Key words and phrases: functions of bounded deformation, Poincaré' s inequality.
Received: 30.05.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 178, Issue 3, Pages 367–372
DOI: https://doi.org/10.1007/s10958-011-0554-9
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: M. Fuchs, S. Repin, “Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient”, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Zap. Nauchn. Sem. POMI, 385, POMI, St. Petersburg, 2010, 224–233; J. Math. Sci. (N. Y.), 178:3 (2011), 367–372
Citation in format AMSBIB
\Bibitem{FucRep10}
\by M.~Fuchs, S.~Repin
\paper Some Poincar\'e-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 385
\pages 224--233
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3907}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 178
\issue 3
\pages 367--372
\crossref{https://doi.org/10.1007/s10958-011-0554-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053532861}
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  • https://www.mathnet.ru/eng/znsl/v385/p224
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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