March  2009, 4(1): 153-175. doi: 10.3934/nhm.2009.4.153

Korn inequalities on thin periodic structures

1. 

Vladimir State Pedagogical University, 11 Stroitelei Avenue, Vladimir, 600024, Russian Federation

2. 

Moscow State Institute of Radioengineering, Electronics and Automatics (Technical University), Russian Federation

Received  December 2008 Revised  December 2008 Published  February 2009

We prove Korn-type inequalities for thin periodic structures of period $\varepsilon$ and thickness $\varepsilon h(\varepsilon)$, where $h(\varepsilon)\to 0$ as $\varepsilon\to 0$, among which there are plane grids, spatial rod and box structures. These inequalities are important in homogenization of corresponding elasticity problems.
Citation: V. V. Zhikov, S. E. Pastukhova. Korn inequalities on thin periodic structures. Networks and Heterogeneous Media, 2009, 4 (1) : 153-175. doi: 10.3934/nhm.2009.4.153
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