Affiliation:
1. Université de Paris and Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions (LJLL), F-75006 Paris, France. E-mails: blanc@ann.jussieu.fr, wolf@math-univ-paris-diderot.fr
Abstract
We study the Poisson equation in a perforated domain with homogeneous Dirichlet boundary conditions. The size of the perforations is denoted by ε > 0, and is proportional to the distance between neighbouring perforations. In the periodic case, the homogenized problem (obtained in the limit ε → 0) is well understood (see (Rocky Mountain J. Math. 10 (1980) 125–140)). We extend these results to a non-periodic case which is defined as a localized deformation of the periodic setting. We propose geometric assumptions that make precise this setting, and we prove results which extend those of the periodic case: existence of a corrector, convergence to the homogenized problem, and two-scale expansion.
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