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 Tr. Mat. Inst. Steklova, 2002, Volume 236, Pages 371–377 (Mi tm308)

Homogenization of Nonlinear Variational Problems by Means of Two-Scale Convergence

S. B. Shulga

Abstract: The theory of two-scale convergence developed in the works of G. Nguetseng, G. Allaire, and V.V. Zhikov is applied to the homogenization of variational problems formulated in terms of measures. A variational problem that describes a nonlinear medium with double porosity is also analyzed.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 236, 357–364

Bibliographic databases:

UDC: 512.54

Citation: S. B. Shulga, “Homogenization of Nonlinear Variational Problems by Means of Two-Scale Convergence”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 371–377; Proc. Steklov Inst. Math., 236 (2002), 357–364

Citation in format AMSBIB
\Bibitem{Shu02} \by S.~B.~Shulga \paper Homogenization of Nonlinear Variational Problems by Means of Two-Scale Convergence \inbook Differential equations and dynamical systems \bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko \serial Tr. Mat. Inst. Steklova \yr 2002 \vol 236 \pages 371--377 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm308} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1931038} \zmath{https://zbmath.org/?q=an:1071.49013} \transl \jour Proc. Steklov Inst. Math. \yr 2002 \vol 236 \pages 357--364 

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This publication is cited in the following articles:
1. Braides A., Piat V.C., Piatnitski A., “A variational approach to double–porosity problems”, Asymptot. Anal., 39:3-4 (2004), 281–308
2. Telega J.J., “Stochastic homogenization: Convexity and nonconvexity”, Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 170, 2004, 305–347
3. A. A. Gavrikov, A. S. Shamaev, “Some problems in acoustics of emulsions”, J. Math. Sci. (N. Y.), 179:3 (2011), 415–436
4. Braides A., Piat V.Ch., Piatnitski A., “Homogenization of Discrete High-Contrast Energies”, SIAM J. Math. Anal., 47:4 (2015), 3064–3091
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