  We study the Poisson equation in a perforated domain with homogeneous
Dirichlet boundary conditions. The size of the perforations is denoted by
$\epsilon$ > 0, and is proportional to the distance between neighbouring
perforations. In the periodic case, the homogenized problem (obtained in the
limit $\epsilon$ $\rightarrow$ 0) is well understood (see [21]). 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.
