A Variational Characterization of the Effective Yield Set for Ionic Polycrystals

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• 作者：Farhod Abdullayev (1)
  Marian Bocea (2)
  Mihai Mih?ilescu (3) (4)
  
• 关键词：$$\mathcal {A}$$ A ; Quasiconvexity ; Effective yield set ; $$\Gamma $$ Γ ; Convergence ; Ionic polycrystals ; Supremal functionals ; 35F99 ; 35J70 ; 49K20 ; 49S05 ; 74C05
• 刊名：Applied Mathematics and Optimization
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：69
• 期：3
• 页码：487-503
• 全文大小：
• 参考文献：1. Bocea, M., Nesi, V.: \(\Gamma \) -Convergence of power-law functionals, variational principles in \(L^\infty \) , and applications. SIAM J. Math. Anal. 39, 1550-576 (2008) CrossRef
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  4. Bocea, M., Mih?ilescu, M., Popovici, C.: On the asymptotic behavior of variable exponent power-law functionals and applications. Ricerche Mat. 59(2), 207-38 (2010) CrossRef
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  8. Dal Maso, G.: An introduction to \(\Gamma \) -convergence. In: Progress in Nonlinear Differential Equations and their Applications, vol. 8. Birk?user, Boston (1993)
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  17. Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer, New York (1994)
  18. Kohn, R.V., Little, T.D.: Some model problems of polycrystal plasticity with deficient basic crystals. SIAM J. Appl. Math. 59, 172-97 (1999) CrossRef
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  20. Tartar, L.: Compensated compactness and applications to partial differential equations. In: Knops, R. (ed.) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. IV. Pitman Research Notes in Mathematics, vol. 39, pp. 136-12. Longman, Harlow (1979)
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• 作者单位：Farhod Abdullayev (1)
  Marian Bocea (2)
  Mihai Mih?ilescu (3) (4)
  
  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA?, 01609, USA
  2. Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, IL?, 60660, USA
  3. Department of Mathematics, University of Craiova, 200585?, Craiova, Romania
  4. Research Group of the Project PN-II-ID-PCE-2011-3-0075, “Simion Stoilow-Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700?, Bucharest, Romania
  
• ISSN：1432-0606

文摘

The effective yield set of ionic polycrystals is characterized by means of variational principles in \(L^\infty \) associated to supremal functionals acting on matrix-valued divergence-free fields.