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Title: On some sharp bounds for the off-diagonal elements of the homogenized tensor (English)
Author: Lukkassen, Dag
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 40
Issue: 5
Year: 1995
Pages: 401-406
Summary lang: English
Category: math
Summary: In this paper we study bounds for the off-diagonal elements of the homogenized tensor for the stationary heat conduction problem. We also state that these bounds are sharp by proving a formula for the homogenized tensor in the case of laminate structures. (English)
Keyword: stationary heat conduction problem
Keyword: $Y$-periodicity
Keyword: homogenized coefficients
Keyword: bounds
Keyword: laminate structures.
MSC: 35B27
MSC: 35Q99
MSC: 73B27
MSC: 73K20
MSC: 74E05
MSC: 74E30
idZBL: Zbl 0847.35011
idMR: MR1342369
DOI: 10.21136/AM.1995.134303
Date available: 2009-09-22T17:49:13Z
Last updated: 2020-07-28
Stable URL:
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Reference: [5] D. Lukkassen: Upper and lower bounds for homogenized coefficients.Uspekhi Mat. Nauk 49 (1994), no. 4, 115.
Reference: [6] D. Lukkassen, L. E. Persson, P. Wall: On some sharp bounds for the effective conductivity.Proceedings from the first International Conference on Composites Engineering (ICCE/1), New Orleans, 1994, pp. 855–856.
Reference: [7] G. W. Milton: On characterizing the set of possible effective tensors of composites: The Variational Method and the Translation Method.Comm. on Pure and Appl. Math. XLIII (1990), 63–125. Zbl 0751.73041, MR 1024190
Reference: [8] L. E. Persson, L. Persson, N. Svanstedt, J. Wyller: The homogenization method: An introduction.Studentlitteratur, Lund, 1993. MR 1250833


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