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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Publié le :
Juan Casado-Díaz 1 ; Julio Couce-Calvo 1 ; José Domingo Martín-Gómez 1
@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/
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