Smoothing effect for Schrödinger boundary value problems
Abstract
Description
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 ($H^{1/2 - ε}$) smoothing effect.
19 pages, various modifications: slight simplifications, typos fixed
19 pages, various modifications: slight simplifications, typos fixed