2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65343We show the necessity of the non trapping condition for the plain smoothing effect ($H^{1/2}$) for Schrödinger equation with Dirichlet boundary conditions in exterior problems. We also give a class of trapped obstacles (Ikawa's example) for which we can prove a weak ($H^{1/2 - ε}$) smoothing effect.19 pages, various modifications: slight simplifications, typos fixedAnalysis of PDEsSpectral Theory35QXX 35LXXtext