Free Access
Issue
ESAIM: COCV
Volume 12, Number 3, July 2006
Page(s) 371 - 397
DOI https://doi.org/10.1051/cocv:2006012
Published online 20 June 2006
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Allaire, Homogenization of the unsteady Stokes equations in porous media, in Progress in Partial Differential Equations: Calculus of Variations, Applications, C. Bandle Ed. Longman, Harlow (1992) 109–123. [Google Scholar]
  3. G. Allaire, Shape Optimization by the Homogenization Method. Springer, New York (2002). [Google Scholar]
  4. G. Allaire and M. Briane, Multiscale convergence and reiterated homogenization. Proc. Roy. Soc. Edinburgh A 126 (1996) 297–342. [Google Scholar]
  5. T. Arbogast, J. Douglas and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21 (1990) 823–836. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.M. Ball and F. Murat, Remarks on Chacon's biting lemma. Proc. Amer. Math. Soc. 107 (1989) 655–663. [MathSciNet] [Google Scholar]
  7. G. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978). [Google Scholar]
  8. A. Bourgeat, S. Luckhaus and A. Mikelić, Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow. SIAM J. Math. Anal. 27 (1996) 1520–1543. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Braides and A. Defranceschi, Homogenization of Multiple Integrals. Oxford University Press, Oxford (1998). [Google Scholar]
  10. J.K. Brooks and R.V. Chacon, Continuity and compactness of measures. Adv. Math. 37 (1980) 16–26. [CrossRef] [Google Scholar]
  11. J. Casado-Diaz and I. Gayte, A general compactness result and its application to two-scale convergence of almost periodic functions. C. R. Acad. Sci. Paris, Ser. I 323 (1996) 329–334. [Google Scholar]
  12. J. Casado-Diaz and I. Gayte, The two-scale convergence method applied to generalized Besicovitch spaces. R. Soc. Lond. Proc., Ser. A 458 (2002) 2925–2946. [Google Scholar]
  13. J. Casado-Diaz, M. Luna-Laynez and J.D. Martin, An adaptation of the multi-scale method for the analysis of very thin reticulated structures. C. R. Acad. Sci. Paris, Ser. I 332 (2001) 223–228. [Google Scholar]
  14. A. Cherkaev, R. Kohn Eds., Topics in the Mathematical Modelling of Composite Materials. Birkhäuser, Boston (1997). [Google Scholar]
  15. D. Cioranescu, A. Damlamian and G. Griso, Periodic unfolding and homogenization. C.R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104. [Google Scholar]
  16. D. Cioranescu and P. Donato, An Introduction to Homogenization. Oxford Univ. Press, New York (1999). [Google Scholar]
  17. C. Conca, J. Planchard and M. Vanninathan, Fluids and Periodic Structures. Wiley, Chichester and Masson, Paris (1995). [Google Scholar]
  18. N. Dunford and J. Schwartz, Linear Operators. Vol. I. Interscience, New York (1958). [Google Scholar]
  19. V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer, Berlin. [Google Scholar]
  20. M. Lenczner, Homogénéisation d'un circuit électrique. C.R. Acad. Sci. Paris, Ser. II 324 (1997) 537–542. [Google Scholar]
  21. M. Lenczner and G. Senouci, Homogenization of electrical networks including voltage-to-voltage amplifiers. Math. Models Meth. Appl. Sci. 9 (1999) 899–932. [CrossRef] [Google Scholar]
  22. J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I. Springer, Berlin, 1972. [Google Scholar]
  23. D. Lukkassen, G. Nguetseng and P. Wall, Two-scale convergence. Int. J. Pure Appl. Math. 2 (2002) 35–86. [MathSciNet] [Google Scholar]
  24. F. Murat and L. Tartar, H-convergence. In [14], 21–44. [Google Scholar]
  25. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet] [Google Scholar]
  26. G. Nguetseng, Asymptotic analysis for a stiff variational problem arising in mechanics. SIAM J. Math. Anal. 21 (1990) 1394–1414. [CrossRef] [MathSciNet] [Google Scholar]
  27. G. Nguetseng, Homogenization structures and applications, I. Zeit. Anal. Anwend. 22 (2003) 73–107. [CrossRef] [Google Scholar]
  28. O.A. Oleĭnik, A.S. Shamaev and G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam (1992). [Google Scholar]
  29. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory. Springer, New York (1980). [Google Scholar]
  30. L. Tartar, Course Peccot. Collège de France, Paris (1977). (Unpublished, partially written in [24]). [Google Scholar]
  31. L. Tartar, Mathematical tools for studying oscillations and concentrations: from Young measures to H-measures and their variants, in Multiscale Problems in Science and Technology. N. Antonić, C.J. van Duijn, W. Jäger, A. Mikelić Eds. Springer, Berlin (2002) 1–84. [Google Scholar]
  32. A. Visintin, Vector Preisach model and Maxwell's equations. Physica B 306 (2001) 21–25. [CrossRef] [Google Scholar]
  33. A. Visintin, Some properties of two-scale convergence. Rendic. Accad. Lincei XV (2004) 93–107. [Google Scholar]
  34. A. Visintin, Two-scale convergence of first-order operators. (submitted) [Google Scholar]
  35. E. Weinan, Homogenization of linear and nonlinear transport equations. Comm. Pure Appl. Math. 45 (1992) 301–326. [CrossRef] [MathSciNet] [Google Scholar]
  36. V.V. Zhikov, On an extension of the method of two-scale convergence and its applications. Sb. Math. 191 (2000) 973–1014. [CrossRef] [MathSciNet] [Google Scholar]

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