## Analysis & PDE

• Anal. PDE
• Volume 6, Number 8 (2013), 1857-1898.

### Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials

Haruya Mizutani

#### Abstract

This paper is concerned with Schrödinger equations with variable coefficients and unbounded electromagnetic potentials, where the kinetic energy part is a long-range perturbation of the flat Laplacian and the electric (respectively magnetic) potential can grow subquadratically (respectively sublinearly) at spatial infinity. We prove sharp (local-in-time) Strichartz estimates, outside a large compact ball centered at the origin, for any admissible pair including the endpoint. Under the nontrapping condition on the Hamilton flow generated by the kinetic energy, global-in-space estimates are also studied. Finally, under the nontrapping condition, we prove Strichartz estimates with an arbitrarily small derivative loss without asymptotic flatness on the coefficients.

#### Article information

Source
Anal. PDE, Volume 6, Number 8 (2013), 1857-1898.

Dates
Received: 25 February 2012
Revised: 24 September 2012
Accepted: 19 January 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731448

Digital Object Identifier
doi:10.2140/apde.2013.6.1857

Mathematical Reviews number (MathSciNet)
MR3198586

Zentralblatt MATH identifier
1297.35061

#### Citation

Mizutani, Haruya. Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials. Anal. PDE 6 (2013), no. 8, 1857--1898. doi:10.2140/apde.2013.6.1857. https://projecteuclid.org/euclid.apde/1513731448

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