Korn inequalities on thin periodic structures

2009, Volume 4, Issue 1: 153-175. doi: 10.3934/nhm.2009.4.153

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1.
Vladimir State Pedagogical University, 11 Stroitelei Avenue, Vladimir, 600024
2.
Moscow State Institute of Radioengineering, Electronics and Automatics (Technical University)

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.
- Dimension theory,
- Poincaré recurrences,
- multifractal analysis
Citation: V. V. Zhikov, S. E. Pastukhova. Korn inequalities on thin periodic structures[J]. Networks and Heterogeneous Media, 2009, 4(1): 153-175. doi: 10.3934/nhm.2009.4.153

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Abstract

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.
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