value problems in domains depending on a small parameter $\epsilon$ in such a way that the limit regions as $\epsilon$ tends to $0$ consist of subsets of different space dimensions. More recently, Maz’ya, Movchan, and Nieves provided the asymptotic analysis of Green’s kernels in domains with small cavities by applying the method of mesoscale asymptotic approximations (cf. [@MaMoNi13]). We also mention Bonnaillie-Noël, Lacave, and Masmoudi [@BoLaMa], Chesnel and Claeys [@ChCl14], and Dauge, Tordeux, and Vial [@DaToVi10].

Problems in perforated domains find several applications in the frame of shape and topological optimization. For a detailed analysis, we refer to Novotny and Sokołowsky [@NoSo13], where the authors analyze the topological derivative to study problems in elasticity and heat diffusion. The topological derivative is indeed defined as the first term of the asymptotic expansion of a given shape functional with respect to a parameter which measures the singular domain perturbation (as, *e.g.*, the diameter of a hole). Moreover, for several applications to inverse problems we refer, *e.g.*, to the monograph Ammari and Kang [@AmKa07].

In particular, boundary value problems in domains with moderately close holes have been deeply studied in Bonnaillie-Noël, Dambrine, Tordeux, and Vial [@BoDaToVi07; @BoDaToVi09], Bonnaillie-Noël and Dambrine [@BoDa13], and Bonnaillie-Noël, 