Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion

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• 作者：S. K. Vodop’yanov ; A. O. Molchanova
• 刊名：Doklady Mathematics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：92
• 期：3
• 页码：739-742
• 全文大小：270 KB
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• 作者单位：S. K. Vodop’yanov (1)
  A. O. Molchanova (1)
  
  1. Sobolev Institute of Mathematics Novosibirsk State University, Siberia, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8362

文摘

We study the problem of minimizing the functional \(I(\phi ) = \int\limits_\Omega {W(x,D\phi )dx}\) on a new class of mappings. We relax summability conditions for admissible deformations to φ ∈ W <sub> n sub> 1 (Ω) and growth conditions on the integrand W(x, F). To compensate for that, we require the condition \(\frac{{\left| {D\phi (x)} \right|^n }} {{J(x,\phi )}} \leqslant M(x) \in L_s (\Omega )\), s > n − 1, on the characteristic of distortion. On assuming that the integrand W(x, F) is polyconvex and coercive, we obtain an existence theorem for the problem of minimizing the functional I(φ) on a new family of admissible deformations A. Original Russian Text © S.K. Vodop’yanov, A.O. Molchanova, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 5, pp. 523–526.Presented by Academician of the RAS Yu.G. Reshetnyak May 15, 2015