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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 385, Pages 224–233
(Mi znsl3907)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl3907 https://www.mathnet.ru/eng/znsl/v385/p224
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Abstract page: | 337 | Full-text PDF : | 92 | References: | 59 |
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