Analysis & PDE

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

On the Schrödinger equation outside strictly convex obstacles

Oana Ivanovici

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Schrödinger equation Strichartz estimates exterior domain


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.

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