Previous |  Up |  Next


Title: On some iterated means arising in homogenization theory (English)
Author: Lukkassen, Dag
Author: Peetre, Jaak
Author: Persson, Lars-Erik
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 49
Issue: 4
Year: 2004
Pages: 343-356
Summary lang: English
Category: math
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. (English)
Keyword: iterations
Keyword: means
Keyword: homogenization theory
MSC: 26A18
MSC: 26D99
MSC: 26E60
MSC: 35M20
idZBL: Zbl 1099.26002
idMR: MR2076489
DOI: 10.1007/s10492-004-6403-0
Date available: 2009-09-22T18:18:29Z
Last updated: 2020-07-02
Stable URL:
Reference: [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
Reference: [2] M.  Avellaneda: Iterated homogenization, differential effective medium theory and applications.Comm. Pure Appl. Math. 40 (1987), 527–554. Zbl 0629.73010, MR 0896766, 10.1002/cpa.3160400502
Reference: [3] E. F.  Beckenbach: Convexity properties of generalized mean value functions.Ann. Math. Statistics 13 (1942), 88–90. Zbl 0061.11601, MR 0006357, 10.1214/aoms/1177731646
Reference: [4] A. Bensoussan, J. L.  Lions, and G. C.  Papanicolaou: Asymptotic Analysis for Periodic Structures.North Holland, Amsterdam-New York-Oxford, 1978. MR 0503330
Reference: [5] J.  Bergh, J.  Löfström: Interpolations Spaces. An introduction (Grundlehren der mathematischen Wissenschaften 223).Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0482275
Reference: [6] W. E.  Boyce, R. C.  Diprima: Elementary Differential Equations and Boundary Value Problems.John Wiley & Sons, New York, 1986. MR 0179403
Reference: [7] A.  Braides, D.  Lukkassen: Reiterated homogenization of integral functionals.Math. Models Methods Appl. Sci. 10 (2000), 47–71. MR 1749689, 10.1142/S0218202500000057
Reference: [8] D. A. G.  Bruggerman: Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen.Ann. Physik. 24 (1935), 634.
Reference: [9] P. S.  Bullen, D. S.  Mitrinović, and P. M.  Vasić: Means and Their Inequalities.D.  Reidel Publishing Company, Dordrecht, 1988. MR 0947142
Reference: [10] G. H.  Hardy, J. E.  Littlewood, and G.  Pólya: Inequalities.Cambridge University Press, Cambridge, 1934 (1978).
Reference: [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.
Reference: [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
Reference: [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. MR 1823125, 10.1142/S0252959901000024
Reference: [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.
Reference: [15] D.  Lukkassen: A new reiterated structure with optimal macroscopic behavior.SIAM J.  Appl. Math. 59 (1999), 1825–1842. Zbl 0933.35023, MR 1710545, 10.1137/S0036139997320081
Reference: [16] J.  Peetre: Generalizing the arithmetic-geometric mean—a hapless computer experiment.Internat. J.  Math. Math. Sci. 12 (1989), 235–245. Zbl 0707.26005, MR 0994905, 10.1155/S016117128900027X
Reference: [17] J.  Peetre: Some observations on algorithms of the Gauss-Borchardt type.Proc. of the Edinburgh Math. Soc. (2) 34 (1991), 415–431. Zbl 0746.39006, MR 1131961


Files Size Format View
AplMat_49-2004-4_3.pdf 1.918Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo