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| Some Remarks on Korn Inequalities |
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Citation： |
Alain DAMLAMIAN.Some Remarks on Korn Inequalities[J].Chinese Annals of Mathematics B,2018,39(2):335~344 |
| Page view： 1409
Net amount： 705 |
Authors： |
Alain DAMLAMIAN; |
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| Abstract： |
A recent joint paper with Doina Cioranescu and Julia Orlik was
concerned with the homogenization of a linearized elasticity problem
with inclusions and cracks (see [Cioranescu, D., Damlamian, A. and
Orlik, J., Homogenization via unfolding in periodic elasticity with
contact on closed and open cracks, {\it Asymptotic Analysis}, {\bf
82}, 2013, 201--232]). It required uniform estimates with respect to
the homogenization parameter. A Korn inequality was used which
involves unilateral terms on the boundaries where a no-penetration
condition is imposed. In this paper, the author presents a general
method to obtain many diverse Korn inequalities including the
unilateral inequalities used in [Cioranescu, D., Damlamian, A. and
Orlik, J., Homogenization via unfolding in periodic elasticity with
contact on closed and open cracks, {\it Asymptotic Analysis}, {\bf
82}, 2013, 201--232]. A preliminary version was presented in
[Damlamian, A., Some unilateral Korn inequalities with application
to a contact problem with inclusions, {\it C. R. Acad. Sci. Paris,
Ser. I}, {\bf 350}, 2012, 861--865]. |
Keywords： |
Korn domains, Korn-Wirtinger domains, Unilateral Korninequality |
Classification： |
35Q74, 74B05, 35J86 |
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