Geodesic
On some sharp bounds for the off-diagonal elements of the homogenized tensor
Applications of Mathematics, Tome 40 (1995) no. 5, pp. 401-406

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

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.
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.
DOI : 10.21136/AM.1995.134303
Classification : 35B27, 35Q99, 73B27, 73K20, 74E05, 74E30
Keywords: stationary heat conduction problem; $Y$-periodicity; homogenized coefficients; bounds; laminate structures. 
Lukkassen, Dag. On some sharp bounds for the off-diagonal elements of the homogenized tensor. Applications of Mathematics, Tome 40 (1995) no. 5, pp. 401-406. doi: 10.21136/AM.1995.134303
@article{10_21136_AM_1995_134303,
     author = {Lukkassen, Dag},
     title = {On some sharp bounds for the off-diagonal elements of the homogenized tensor},
     journal = {Applications of Mathematics},
     pages = {401--406},
     year = {1995},
     volume = {40},
     number = {5},
     doi = {10.21136/AM.1995.134303},
     mrnumber = {1342369},
     zbl = {0847.35011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134303/}
}
TY  - JOUR
AU  - Lukkassen, Dag
TI  - On some sharp bounds for the off-diagonal elements of the homogenized tensor
JO  - Applications of Mathematics
PY  - 1995
SP  - 401
EP  - 406
VL  - 40
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134303/
DO  - 10.21136/AM.1995.134303
LA  - en
ID  - 10_21136_AM_1995_134303
ER  - 
%0 Journal Article
%A Lukkassen, Dag
%T On some sharp bounds for the off-diagonal elements of the homogenized tensor
%J Applications of Mathematics
%D 1995
%P 401-406
%V 40
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134303/
%R 10.21136/AM.1995.134303
%G en
%F 10_21136_AM_1995_134303

[1] A. Bensoussan, J. L. Lions, G. Papanicolaou: Asymptotic analysis for periodic structures. North-Holland, Amsterdam, 1978. | MR

[2] L. V. Gibiansky: Bounds on effective moduli of composite materials. Lecture notes, School on Homogenization, ICTP, Trieste, 1993.

[3] Z. Hashin, S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multi phase materials. J. Appl. Phys. 33 (1962), 3125–3131. | DOI

[4] C. Johnson: Numerical solution of partial differential equations by the finite element method. Studentlitteratur, Lund, 1987. | MR | Zbl

[5] D. Lukkassen: Upper and lower bounds for homogenized coefficients. Uspekhi Mat. Nauk 49 (1994), no. 4, 115.

[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.

[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. | MR | Zbl

[8] L. E. Persson, L. Persson, N. Svanstedt, J. Wyller: The homogenization method: An introduction. Studentlitteratur, Lund, 1993. | MR

Cité par Sources :