Affiliations: Commissariat à l'Energie Atomique, LETR / SERMA / DMT, C.E.N. Saclay, 91191 Gif sur Yvette, France | Laboratoire d'Analyse Numérique, Tour 55–65, Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France
Note: [] With an appendix written jointly with A.K. Nandakumar, TIFR, P.B. 1234, Indian Institute of Science, Bangalore 560 012, India.
Note: [] Correspondence to: G. Allaire, Commissariat à l'Energie Atomique, LETR/SERMA/DMT, C.E.N. Saday, 91191 Gif sur Yvette, France.
Abstract: We consider the homogenization of second-order elliptic equations with a Neumann boundary condition in open sets periodically perforated with holes of the size of the period. When the holes are isolated, Cioranescu and Saint Jean Paulin (1979) proved the convergence of the homogenization process. One of their main tool was the construction of an extension of the solution, which is uniformly bounded. In the present paper, we give a new proof of the convergence, which avoids the use of such an extension. The main advantage of our approach is that it generalizes the result of Cioranescu and Saint Jean Paulin to the general case of periodic holes which may be not isolated (including, for example in three dimensions, the case of a domain perforated by interconnected cylinders).
