Smoothing effect for Schrödinger boundary value problems

Abstract

We 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 ($H^{1/2-\epsilon }$) smoothing effect.

19 pages, various modifications: slight simplifications, typos fixed