We prove sharp Strichartz estimates for the semiclassical Schrödinger equation on a compact Riemannian manifold with a smooth, strictly geodesically concave boundary. We deduce classical Strichartz estimates for the Schrödinger equation outside a strictly convex obstacle, local existence for the -critical (quintic) Schrödinger equation, and scattering for the subcritical Schrödinger equation in three dimensions.
"On the Schrödinger equation outside strictly convex obstacles." Anal. PDE 3 (3) 261 - 293, 2010. https://doi.org/10.2140/apde.2010.3.261