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Smoothing effect for Schrödinger boundary value problems

Nicolas Burq
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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 ($H^{1/2 - ε}$) smoothing effect.

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Nicolas Burq. 2003-08-25. Smoothing effect for Schrödinger boundary value problems. https://arxiv.org/abs/math/0210279

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