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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.
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.
Casado-Díaz, Juan 1 ; Couce-Calvo, Julio 1 ; Martín-Gómez, José Domingo 1
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/articles/10.1016/j.crma.2005.12.021/
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