[Un résultat sur la variation d'un matériau en fonction de petites inclusions]
On considère une famille de matériaux obtenus par homogénéisation consistant à remplacer une petite partie de matériau, de taille ɛ, par d'autres matériaux. Dans un article antérieur on a caractérisé un sous-ensemble de l'ensemble des « dérivées », par rapport à ɛ de cette famille, pour . Dans cette Note on démontre que ce sous-ensemble est en fait dense. Le résultat peut être appliqué, par exemple, à l'obtention des conditions d'optimalité pour des matériaux composites.
We consider the family of materials obtained, via homogenization, by replacing a small portion, of size ɛ, of a fixed material by other materials. In a previous paper we have obtained a subset of the set of ‘derivatives’ of this family with respect to ɛ in . In the present Note we prove that this set is, in fact, dense. This result can be applied, for example, to obtain optimality conditions for composite materials.
Accepté le :
Publié le :
@article{CRMATH_2006__342_5_353_0,
author = {Juan Casado-D{\'\i}az and Julio Couce-Calvo and Jos\'e Domingo Mart{\'\i}n-G\'omez},
title = {A density result for the variation of a material with respect to small inclusions},
journal = {Comptes Rendus. Math\'ematique},
pages = {353--358},
publisher = {Elsevier},
volume = {342},
number = {5},
year = {2006},
doi = {10.1016/j.crma.2005.12.021},
language = {en},
}
TY - JOUR AU - Juan Casado-Díaz AU - Julio Couce-Calvo AU - José Domingo Martín-Gómez TI - A density result for the variation of a material with respect to small inclusions JO - Comptes Rendus. Mathématique PY - 2006 SP - 353 EP - 358 VL - 342 IS - 5 PB - Elsevier DO - 10.1016/j.crma.2005.12.021 LA - en ID - CRMATH_2006__342_5_353_0 ER -
%0 Journal Article %A Juan Casado-Díaz %A Julio Couce-Calvo %A José Domingo Martín-Gómez %T A density result for the variation of a material with respect to small inclusions %J Comptes Rendus. Mathématique %D 2006 %P 353-358 %V 342 %N 5 %I Elsevier %R 10.1016/j.crma.2005.12.021 %G en %F CRMATH_2006__342_5_353_0
Juan Casado-Díaz; Julio Couce-Calvo; José Domingo Martín-Gómez. A density result for the variation of a material with respect to small inclusions. Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 353-358. doi : 10.1016/j.crma.2005.12.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.021/
[1] Shape Optimization by the Homogenization Method, Appl. Math. Sci., vol. 146, Springer-Verlag, New York, 2002
[2] Optimality conditions for nonconvex multistate control problems in the coefficients, SIAM J. Control Optim., Volume 43 (2004) no. 1, pp. 216-239
[3] Variational Methods for Structural Optimization, Appl. Math. Sci., vol. 140, Springer-Verlag, New York, 2000
[4] G. Dal Maso, R.V. Kohn, The local character of G-closure, Unpublished work
[5] Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994
[6] An -estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 3 (1963) no. 17, pp. 189-206
[7] H-convergence (A. Cherkaev; R. Kohn, eds.), Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl., Birkhäuser, Boston, 1997, pp. 21-44
[8] Calculus of variations (A. Cherkaev; R. Kohn, eds.), Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl., Birkhäuser, Boston, 1997, pp. 139-173
[9] Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1984
[10] An Introduction to the homogenization method in optimal design, CIM/CIME, Summer School, Trôia, 1–6 June 1998 (A. Cellina; A. Ornelas, eds.) (Lecture Notes in Math.), Volume vol. 1740, Springer-Verlag, Berlin (2000), pp. 47-156
Cité par Sources :
Commentaires - Politique
Dirichlet problems with skew-symmetric drift terms
Lucio Boccardo; Juan Casado-Diaz; Luigi Orsina
C. R. Math (2024)