Open AccessKorn inequalities on thin periodic structures
Author(s) -
В. В. Жиков,
S. E. Pastukhova
Publication year - 2009
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2009.4.153
Subject(s) - homogenization (climate) , mathematics , inequality , mathematical analysis , pure mathematics , physics , biodiversity , ecology , biology
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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