#### Vol. 3, No. 3, 2010

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Ethics Statement Contacts Author Index To Appear ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print)
On the Schrödinger equation outside strictly convex obstacles

### Oana Ivanovici

Vol. 3 (2010), No. 3, 261–293
##### Abstract

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 ${H}^{1}$-critical (quintic) Schrödinger equation, and scattering for the subcritical Schrödinger equation in three dimensions.

##### Keywords
Schrödinger equation, Strichartz estimates, exterior domain
##### Mathematical Subject Classification 2000
Primary: 35Q55, 37K05, 37K50