On the Schrodinger equation outside strictly convex obstacles

@inproceedings{Ivanovici2008OnTS,
  title={On the Schrodinger equation outside strictly convex obstacles},
  author={Oana Ivanovici},
  year={2008}
}
We prove sharp Strichartz estimates for the semi-classical Schrödinger equation on a compact Riemannian manifold with smooth, strictly geodesically concave boundary. We deduce classical Strichartz estimates for the Schrödinger equation outside a strictly convex obstacle, local existence for the H1-critical (quintic) Schrödinger equation and scattering for the sub-critical Schrödinger equation in 3D. 

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