Korn inequalities on thin periodic structures

V. V. Zhikov; S. E. Pastukhova

doi:10.3934/nhm.2009.4.153

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

This issue Previous Article Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem Next Article

Korn inequalities on thin periodic structures

V. V. Zhikov^1, and
S. E. Pastukhova^2,

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

Received: November 30, 2008

Revised: November 30, 2008

Published: February 2009

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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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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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