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2013 Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials
Haruya Mizutani
Anal. PDE 6(8): 1857-1898 (2013). DOI: 10.2140/apde.2013.6.1857

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.

Citation

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Haruya Mizutani. "Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials." Anal. PDE 6 (8) 1857 - 1898, 2013. https://doi.org/10.2140/apde.2013.6.1857

Information

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

zbMATH: 1297.35061
MathSciNet: MR3198586
Digital Object Identifier: 10.2140/apde.2013.6.1857

Subjects:
Primary: 35B45 , 35Q41
Secondary: 35S30 , 81Q20

Keywords: asymptotically flat metric , Schrödinger equation , Strichartz estimates , unbounded electromagnetic potentials , unbounded potential

Rights: Copyright © 2013 Mathematical Sciences Publishers

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Vol.6 • No. 8 • 2013
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