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Keywords:
iterations; means; homogenization theory
iterations; means; homogenization theory
Summary:
We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.
References:
[1] J. Arazy, T. Claesson, S. Janson and J. Peetre: Means and their iterations. In: Proceedings of the Nineteenth Nordic Congress of Mathematics, Reykjavik, 1984, pp. 191–212. MR 0828035
[2] M. Avellaneda: Iterated homogenization, differential effective medium theory and applications. Comm. Pure Appl. Math. 40 (1987), 527–554. DOI 10.1002/cpa.3160400502 | MR 0896766 | Zbl 0629.73010
[3] E. F. Beckenbach: Convexity properties of generalized mean value functions. Ann. Math. Statistics 13 (1942), 88–90. DOI 10.1214/aoms/1177731646 | MR 0006357 | Zbl 0061.11601
[4] A. Bensoussan, J. L. Lions, and G. C. Papanicolaou: Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam-New York-Oxford, 1978. MR 0503330
[5] J. Bergh, J. Löfström: Interpolations Spaces. An introduction (Grundlehren der mathematischen Wissenschaften 223). Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0482275
[6] W. E. Boyce, R. C. Diprima: Elementary Differential Equations and Boundary Value Problems. John Wiley & Sons, New York, 1986. MR 0179403
[7] A. Braides, D. Lukkassen: Reiterated homogenization of integral functionals. Math. Models Methods Appl. Sci. 10 (2000), 47–71. DOI 10.1142/S0218202500000057 | MR 1749689
[8] D. A. G. Bruggerman: Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. Ann. Physik. 24 (1935), 634.
[9] P. S. Bullen, D. S. Mitrinović, and P. M. Vasić: Means and Their Inequalities. D. Reidel Publishing Company, Dordrecht, 1988. MR 0947142
[10] G. H. Hardy, J. E. Littlewood, and G. Pólya: Inequalities. Cambridge University Press, Cambridge, 1934 (1978).
[11] Z. Hashin, S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multiphase materials. J. Appl. Phys. 33 (1962), 3125–3131.
[12] J.-L. Lions, D. Lukkassen, L.-E. Persson, and P. Wall: Reiterated homogenization of monotone operators. C. R. Acad. Sci. Paris, Sér. I, Math. 330 (2000), 675–680. MR 1763909
[13] J.-L. Lions, D. Lukkassen, L.-E. Persson, and P. Wall: Reiterated homogenization of nonlinear monotone operators. Chinese Ann. Math. Ser. B 22 (2001), 1–12. DOI 10.1142/S0252959901000024 | MR 1823125
[14] D. Lukkassen: Formulæ and bounds connected to homogenization and optimal design of partial differential operators and integral functionals. PhD thesis (ISBN: 82-90487-87-8), University of Tromsø, 1996.
[15] D. Lukkassen: A new reiterated structure with optimal macroscopic behavior. SIAM J. Appl. Math. 59 (1999), 1825–1842. DOI 10.1137/S0036139997320081 | MR 1710545 | Zbl 0933.35023
[16] J. Peetre: Generalizing the arithmetic-geometric mean—a hapless computer experiment. Internat. J. Math. Math. Sci. 12 (1989), 235–245. DOI 10.1155/S016117128900027X | MR 0994905 | Zbl 0707.26005
[17] J. Peetre: Some observations on algorithms of the Gauss-Borchardt type. Proc. of the Edinburgh Math. Soc. (2) 34 (1991), 415–431. MR 1131961 | Zbl 0746.39006
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