# American Institute of Mathematical Sciences

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