[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.
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@article{CRMATH_2006__342_5_353_0,
author = {Casado-D{\'\i}az, Juan and Couce-Calvo, Julio and Mart{\'\i}n-G\'omez, Jos\'e Domingo},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.021/}
}
TY - JOUR AU - Casado-Díaz, Juan AU - Couce-Calvo, Julio AU - Martín-Gómez, José Domingo 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2005.12.021/ DO - 10.1016/j.crma.2005.12.021 LA - en ID - CRMATH_2006__342_5_353_0 ER -
%0 Journal Article %A Casado-Díaz, Juan %A Couce-Calvo, Julio %A Martín-Gómez, José Domingo %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 %U http://www.numdam.org/articles/10.1016/j.crma.2005.12.021/ %R 10.1016/j.crma.2005.12.021 %G en %F CRMATH_2006__342_5_353_0
Casado-Díaz, Juan; Couce-Calvo, Julio; Martín-Gómez, José Domingo. A density result for the variation of a material with respect to small inclusions. Comptes Rendus. Mathématique, Tome 342 (2006) no. 5, pp. 353-358. doi : 10.1016/j.crma.2005.12.021. http://www.numdam.org/articles/10.1016/j.crma.2005.12.021/
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