Smoothing effect for Schr\"odinger boundary value problems

Nicolas Burq

Smoothing effect for Schr\"odinger boundary value problems

偏微分方程分析 2007-05-23 v2 谱理论

作者: Nicolas Burq

摘要

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.

关键词

schrödinger equation nonlinear schrödinger equation boundary value problems

引用

@article{arxiv.math/0210279,
  title  = {Smoothing effect for Schr\"odinger boundary value problems},
  author = {Nicolas Burq},
  journal= {arXiv preprint arXiv:math/0210279},
  year   = {2007}
}

备注

19 pages, various modifications: slight simplifications, typos fixed

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