Comptes Rendus
Numerical Analysis/Calculus of Variations
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.

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 ɛ=0. 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 ɛ=0. 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.12.021

Juan Casado-Díaz 1; Julio Couce-Calvo 1; José Domingo Martín-Gómez 1

1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, c/Tarfia s/n, 41012 Sevilla, Spain
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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/

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