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Korn's inequality for periodic solids and convergence rate of homogenization

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Abstract:

In a three-dimensional solid with arbitrary periodic Lipschitz perforation the Korn inequality is proved with a constant independent of the perforation size. The convergence rate of homogenization as a function of the Sobolev-Slobodetskii smoothness of data is also estimated. We improve foregoing results in elasticity dropping customary restrictions on the shape of the periodicity cell and superfluous smoothness and smallness assumptions on the external forces and traction.

Keywords: Korn's inequality; convergence rate; homogenization

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810903042174

Affiliations: 1: Department of Engineering, University of Sannio, 82100 Benevento, Italy 2: University of Cassino, DAEIMI, Cassino (FR), Italy 3: Institute of Mechanical Engineering Problems, Russian Academy of Science, 199178, St. Petersburg, Russia

Publication date: 2009-06-01

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