Analysis & PDE

  • Anal. PDE
  • Volume 3, Number 3 (2010), 261-293.

On the Schrödinger equation outside strictly convex obstacles

Oana Ivanovici

Full-text: Open access

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.

Article information

Source
Anal. PDE, Volume 3, Number 3 (2010), 261-293.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731078

Digital Object Identifier
doi:10.2140/apde.2010.3.261

Mathematical Reviews number (MathSciNet)
MR2672795

Zentralblatt MATH identifier
1222.35186

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 37K05: Hamiltonian structures, symmetries, variational principles, conservation laws 37K50: Bifurcation problems

Keywords
Schrödinger equation Strichartz estimates exterior domain

Citation

Ivanovici, Oana. On the Schrödinger equation outside strictly convex obstacles. Anal. PDE 3 (2010), no. 3, 261--293. doi:10.2140/apde.2010.3.261. https://projecteuclid.org/euclid.apde/1513731078


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