Journal of the Mathematical Society of Japan

Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity

Haruya MIZUTANI

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Abstract

In the present paper we consider Schrödinger equations with variable coefficients and potentials, where the principal part is a long-range perturbation of the flat Laplacian and potentials have at most linear growth at spatial infinity. We then prove local-in-time Strichartz estimates, outside a large compact set centered at origin, without loss of derivatives. Moreover we also prove global-in-space Strichartz estimates under the non-trapping condition on the Hamilton flow generated by the kinetic energy.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 3 (2013), 687-721.

Dates
First available in Project Euclid: 23 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1374586621

Digital Object Identifier
doi:10.2969/jmsj/06530687

Mathematical Reviews number (MathSciNet)
MR3084976

Zentralblatt MATH identifier
1273.35232

Subjects
Primary: 35Q41: Time-dependent Schrödinger equations, Dirac equations
Secondary: 81Q20: Semiclassical techniques, including WKB and Maslov methods

Keywords
Strichartz estimates Schrödinger equation unbounded potential

Citation

MIZUTANI, Haruya. Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity. J. Math. Soc. Japan 65 (2013), no. 3, 687--721. doi:10.2969/jmsj/06530687. https://projecteuclid.org/euclid.jmsj/1374586621


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