\Omega^i_1\cap\Omega^i_2 \cap \Omega^o$}.
\end{split}$$ The letter ‘$i$’ stands for ‘inner’ and the letter ‘$o$’ stands for ‘outer’. The symbol ‘${\mathrm{cl}}$’ denotes the closure. The set $\Omega^o$ will play the role of the ‘unperturbed’ domain, where we make two perforations of the shape of $\Omega^i_1$ and of $\Omega^i_2$, respectively. We also fix two points $$\label{p}
p^1, p^2 \in \Omega^o\, ,\qquad p^1 \neq p^2\, .$$ Then we take $\epsilon_0>0$ and a function $\eta$ from $]0,\epsilon_0[$ to $]0,+\infty[$ such that $$\label{eta}
\lim_{\epsilon\to 0^+}\eta(\epsilon)=0 \qquad \text{and} \qquad \lim_{\epsilon \to 0^+} \frac{\epsilon}{\eta(\epsilon)}=r_\ast \in [0,+\infty[\, .$$ The function $\eta$ will control the distance between the holes, while the parameter $\epsilon$ will determine their size. We assume that $$\label{assrast}
\left(p^1+r_\ast\mathrm{cl}\Omega^i_1\right)\cap\left(p^2+r_\ast\mathrm{cl}\Omega^i_2\right)= \emptyset\, .$$ Possibly shrinking $\epsilon_0$, we may also assume that $$\label{e0}
\begin{split}
&\left(p^1+\frac{\epsilon}{\eta(\epsilon)}\mathrm{cl}\Omega^i_1\right)\cap\left(p^2+\frac{\epsilon}{\eta(\epsilon)}\mathrm{cl}\Omega^i_2\right)= \emptyset  \qquad \forall \epsilon \in ]0,\epsilon_0[\, ,\\
&\bigg (\eta(\epsilon)p^1+\epsilon\mathrm{cl}\Omega^i_1\bigg)\cup\bigg(\eta(\epsilon)p^2+\epsilon\mathrm{cl}\Omega^i_2\bigg) \subseteq \Omega^o \qquad \forall \epsilon \in ]0,\epsilon_0[\, .
\end{split}$$ Then we introduce the perforated domain $$\Omega_{\epsilon}\equiv \Omega^o \setminus  \bigcup_{j=1}^2 \bigg (\eta(\epsilon)p^j+\epsilon\mathrm{cl}\Omega^i_j\bigg) \qquad \forall \epsilon\in ]0,\epsilon_{0}[\, .$$ In other words, the set $\Omega_{\epsilon}$ is obtained by removing from $\Omega^o$ the two sets $\eta(\epsilon)p^1+\epsilon\mathrm{cl}\Omega^i_1$ and $\eta(\epsilon)p^2+\epsilon\mathrm{cl}\Omega^i_2$. As $\epsilon \to 0^+$, both the size of the perforations and their distance tend to $0$. Next, for each $\epsilon$ positive 