In this paper we give a general presentation of
the homogenization of Neumann type problems in periodically perforated
domains, including the case where the shape of the reference hole
varies with the size
of the period (in the spirit of the construction of self-similar fractals).
We shows that H0-convergence holds under the extra assumption that
there exists a bounded sequence of extension operators for
the reference holes. The general class
of Jones-domains gives an example where this result applies.
When this assumption fails, another approach, using
the Poincaré–Wirtinger
inequality is presented. A corresponding class where it applies
is that of John-domains, for which the Poincaré–Wirtinger constant
is controlled.
The relationship between these two kinds of assumptions is also clarified.