Geodesic
Some Poincar\'e-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 224-233

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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. 
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     author = {M. Fuchs and S. Repin},
     title = {Some {Poincar\'e-type} inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {224--233},
     publisher = {mathdoc},
     volume = {385},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a10/}
}
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M. Fuchs; S. Repin. Some Poincar\'e-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 224-233. http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a10/