Mathematics – Analysis of PDEs
Scientific paper
2002-10-17
Mathematics
Analysis of PDEs
19 pages, various modifications: slight simplifications, typos fixed
Scientific paper
We show the necessity of the non trapping condition for the plain smoothing
effect ($H^{1/2}$) for Schr\"odinger 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.
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