In this paper we give a general presentation ofthe homogenization of Neumann type problems in periodically perforateddomains, including the case where the shape of the reference hole varies with the sizeof the period (in the spirit of the construction of self-similar fractals).We shows that H 0-convergence holds under the extra assumption thatthere exists a bounded sequence of extension operators forthe reference holes. The general classof Jones-domains gives an example where this result applies. When this assumption fails, another approach, usingthe Poincaré–Wirtingerinequality is presented. A corresponding class where it appliesis that of John-domains, for which the Poincaré–Wirtinger constantis controlled.The relationship between these two kinds of assumptions is also clarified.
