is a critical point of the Robin function of (the diagonal ofthe regular part of the Green function), answering to a conjecture by Brezis andPeletier in [3], in which was analyzed the same problem in the case of being aspherical domain.In order to obtain this concentration result, even without localizing the blowing-up, the cited authors also utilize some standard elliptic regularity techniques thatrequire to work in smooth domains.We also stress that regularity assumptions on the domain have a strong impacton concentration results. In fact, in the case of smooth domains, the Robin functionhas no critical points in a neighborhood of the boundary and thus in [3,8,15]concentration may occur only in . In [7], Flucher, Garroni and Muller wereable to construct an example of a nonsmooth domain , with its Robin function~achieving its in mum on the boundary; and then Pistoia and Rey showed thatconcentration can occur on the boundary, analyzing the asymptotic behavior ofthe maximizing solutions of the elliptic Dirichlet problem (1.2) in such (see [~ 13]).Here we can obtain the same concentration result in general bounded domain,not depending from any strong hypotheses of regularity, as a consequence of Li-ons’ Concentration-compactness principle ([10]) together with the convergence ofmaxF