Abstract and Applied Analysis

Homogenization of Elliptic Differential Equations in One-Dimensional Spaces

G. Grammel

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Linear elliptic differential equations with periodic coefficients in one-dimensional domains are considered. The approximation properties of the homogenized system are investigated. For H 1 -data, it turns out that the order of approximation is strongly related to the decay of the Fourier coefficients of the L 2 -functions involved.

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Abstr. Appl. Anal., Volume 2007 (2007), Article ID 98538, 6 pages.

First available in Project Euclid: 27 February 2008

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Grammel, G. Homogenization of Elliptic Differential Equations in One-Dimensional Spaces. Abstr. Appl. Anal. 2007 (2007), Article ID 98538, 6 pages. doi:10.1155/2007/98538. https://projecteuclid.org/euclid.aaa/1204126585

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  • D. Cioranescu and P. Donato, An Introduction to Homogenization, vol. 17 of Oxford Lecture Series in Mathematics and Its Applications, The Clarendon Press, Oxford University Press, New York, NY, USA, 1999.
  • L. Tartar, ``Compensated compactness and applications to partial differential equations,'' in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, R. J. Knops, Ed., vol. 39 of Research Notes in Mathematics, pp. 136--212, Pitman, Boston, Mass, USA, 1979.
  • G. Allaire, ``Homogenization and two-scale convergence,'' SIAM Journal on Mathematical Analysis, vol. 23, no. 6, pp. 1482--1518, 1992.
  • A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, vol. 5 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, The Netherlands, 1978.
  • C. Conca and F. Lund, ``Fourier homogenization method and the propagation of acoustic waves through a periodic vortex array,'' SIAM Journal on Applied Mathematics, vol. 59, no. 5, pp. 1573--1581, 1999.
  • A. Zygmund, Trigonometric Series. Vol. I, II, Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 3rd edition, 2002.