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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)



Asymptotics of the solution of the problem of deformation of an arbitrary locally periodic thin plate

Authors: E. A. Akimova, S. A. Nazarov and G. A. Chechkin
Translated by: H. H. McFaden
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 65 (2004).
Journal: Trans. Moscow Math. Soc. 2004, 1-29
MSC (2000): Primary 74K20, 35B40; Secondary 35J55, 74B15, 74E30, 74E10, 35Q72
Published electronically: November 2, 2004
MathSciNet review: 2193435
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Abstract: This paper is concerned with a problem in the theory of elasticity for a thin composite plate. The principal terms are constructed for the asymptotics of the solution, with only local periodicity of the elastic moduli of the material and the shape of the plate assumed. The asymptotic expression is justified with the help of a weighted anisotropic Korn's inequality, which is proved by means of the ``tetris'' procedure for constructing a supporting set.

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Additional Information

E. A. Akimova
Affiliation: Moscow State University, Department of Mechanics and Mathematics, Moscow 119899, Russia

S. A. Nazarov
Affiliation: St. Petersburg State University, St. Petersburg, Russia

G. A. Chechkin
Affiliation: Moscow State University, Department of Mechanics and Mathematics, Moscow 119899, Russia

Published electronically: November 2, 2004
Additional Notes: The work of S. A. Nazarov and G. A. Chechkin was supported in part by the Russian Foundation for Basic Research (grants no. 00–01–00455 and 02–01–00693, and 02–01–00868, respectively).
Article copyright: © Copyright 2004 American Mathematical Society