In the introduction the authors review the blow-up results as \(\epsilon\downarrow 0\) concerning the problem \[ -\Delta u=u^{p-\epsilon},\quad u>0 {\text{ in } } \Omega \]
\[ u=0 {\text{ on }}\partial \Omega \] with \(p=(N+2)/(N-2),\) \(N\geq 3\), when \(\Omega\) is a smooth domain. They focus on the property that the solution \(u_\epsilon\) concentrates at a specific point. The aim of the paper is to extend such results to the case in which \(\Omega\) is the non-smooth domain \(\tilde{\Omega}\) defined through an induction procedure by M. Flucher, A. Garroni and S. Müller [Calc. Var. Partial Differ. Equ. 14, No. 4, 483–516 (2002; Zbl 1004.35040)]. They also show that, contrary to the case of smooth domains, the concentration point belongs to the boundary of \(\tilde{\Omega}\).