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Networks and Heterogeneous Media

2009, Volume 4, Issue 1: 153-175. doi: 10.3934/nhm.2009.4.153
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Korn inequalities on thin periodic structures

  • 1.
    Vladimir State Pedagogical University, 11 Stroitelei Avenue, Vladimir, 600024
  • 2.
    Moscow State Institute of Radioengineering, Electronics and Automatics (Technical University)
  • Received: 01 December 2008 Revised: 01 December 2008

  • Primary: 58F15, 58F17; Secondary: 53C35.

  • We prove Korn-type inequalities for thin periodic structures of period ε and thickness εh(ε), where h(ε)→0 as ε→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[J]. Networks and Heterogeneous Media, 2009, 4(1): 153-175. doi: 10.3934/nhm.2009.4.153

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  • We prove Korn-type inequalities for thin periodic structures of period ε and thickness εh(ε), where h(ε)→0 as ε→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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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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