Free Access
Volume 16, Number 1, January-March 2010
Page(s) 148 - 175
Published online 19 December 2008
  1. E. Acerbi, V. Chiadò Piat, G. Dal Maso and D. Percivale, An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal. 18 (1992) 481–496. [CrossRef] [MathSciNet]
  2. R.A. Adams, Sobolev spaces. Academic Press, New York (1975).
  3. A.G. Belyaev, G.A. Chechkin and A.L. Piatnitski, Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary. Sib. Math. J. 39 (1998) 621–644. [CrossRef]
  4. A.G. Belyaev, G.A. Chechkin and A.L. Piatnitski, Homogenization of second-order elliptic operators in a perforated domain with oscillating Fourier boundary conditions. Sb. Math. 192 (2001) 933–949. [CrossRef] [MathSciNet]
  5. A. Braides and A. Defranceschi, Homogenization of multiple integrals, Oxford Lecture Series in Mathematics and its Applications 12. The Clarendon Press, Oxford University Press, New York (1998).
  6. A. Brillard, Asymptotic analysis of two elliptic equations with oscillating terms. RAIRO Modél. Math. Anal. Numér. 22 (1988) 187–216. [MathSciNet]
  7. D. Cioranescu and P. Donato, On a Robin problem in perforated domains, in Homogenization and applications to material sciences, D. Cioranescu et al. Eds., GAKUTO International Series, Mathematical Sciences and Applications 9, Tokyo, Gakkotosho (1997) 123–135.
  8. D. Cioranescu and F. Murat, A strange term coming from nowhere, in Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl. 31, Birkhauser, Boston (1997) 45–93.
  9. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes. J. Math. Anal. Appl. 71 (1979) 590–607. [CrossRef] [MathSciNet]
  10. D. Cioranescu and J. Saint Jean Paulin, Truss structures: Fourier conditions and eigenvalue problems, in Boundary control and boundary variation, J.P. Zolezio Ed., Lecture Notes Control Inf. Sci. 178, Springer-Verlag (1992) 125–141.
  11. C. Conca, On the application of the homogenization theory to a class of problems arising in fluid mechanics. J. Math. Pures Appl. 64 (1985) 31–75. [MathSciNet]
  12. G. Dal Maso, An introduction to Γ-convergence. Birkhauser, Boston (1993).
  13. V.A. Marchenko and E.Y. Khruslov, Boundary value problems in domains with fine-grained boundaries. Naukova Dumka, Kiev (1974).
  14. V.A. Marchenko and E.Y. Khruslov, Homogenization of partial differential equations. Birkhauser (2006).
  15. O.A. Oleinik and T.A. Shaposhnikova, On an averaging problem in a partially punctured domain with a boundary condition of mixed type on the boundary of the holes, containing a small parameter. Differ. Uravn. 31 (1995) 1150–1160, 1268. Translation in Differ. Equ. 31 (1995) 1086–1098.
  16. O.A. Oleinik and T.A. Shaposhnikova, On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary. Rend. Mat. Acc. Linceis. IX 7 (1996) 129–146.
  17. S.E. Pastukhova, Tartar's compensated compactness method in the averaging of the spectrum of a mixed problem for an elliptic equation in a punctured domain with a third boundary condition. Sb. Math. 186 (1995) 753–770. [CrossRef] [MathSciNet]
  18. S.E. Pastukhova, On the character of the distribution of the temperature field in a perforated body with a given value on the outer boundary under heat exchange conditions on the boundary of the cavities that are in accord with Newton's law. Sb. Math. 187 (1996) 869–880. [CrossRef] [MathSciNet]
  19. S.E. Pastukhova, Spectral asymptotics for a stationary heat conduction problem in a perforated domain. Mat. Zametki 69 (2001) 600–612 [in Russian]. Translation in Math. Notes 69 (2001) 546–558.
  20. W.P. Ziemer, Weakly differentiable functions. Springer-Verlag, New York (1989).

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