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2010 On the Schrödinger equation outside strictly convex obstacles
Oana Ivanovici
Anal. PDE 3(3): 261-293 (2010). 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 H1-critical (quintic) Schrödinger equation, and scattering for the subcritical Schrödinger equation in three dimensions.

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Oana Ivanovici. "On the Schrödinger equation outside strictly convex obstacles." Anal. PDE 3 (3) 261 - 293, 2010. https://doi.org/10.2140/apde.2010.3.261

Information

Received: 16 January 2009; Revised: 13 August 2009; Accepted: 12 September 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1222.35186
MathSciNet: MR2672795
Digital Object Identifier: 10.2140/apde.2010.3.261

Subjects:
Primary: 35Q55, 37K05, 37K50

Rights: Copyright © 2010 Mathematical Sciences Publishers

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