On the Schrödinger equation outside strictly convex obstacles

Ivanovici, Oana

doi:10.2140/apde.2010.3.261

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On the Schrödinger equation outside strictly convex obstacles

Oana Ivanovici

Vol. 3 (2010), No. 3, 261–293

DOI: 10.2140/apde.2010.3.261

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

Milestones

Received: 16 January 2009

Revised: 13 August 2009

Accepted: 12 September 2009

Published: 21 July 2010

Authors

Oana Ivanovici
Johns Hopkins University Department of Mathematics Baltimore, MD 21218 United States

Vol. 3, No. 3, 2010