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Strichartz estimates
for Schrödinger equations with variable coefficients and
unbounded potentials
Haruya Mizutani |
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Vol. 6 (2013), No. 8, 1857–1898
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Abstract |
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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. |
Keywords
Schrödinger equation, Strichartz estimates, asymptotically
flat metric, unbounded potential, unbounded electromagnetic
potentials
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Mathematical Subject Classification 2010
Primary: 35B45, 35Q41
Secondary: 35S30, 81Q20
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Milestones
Received: 25 February 2012
Revised: 24 September 2012
Accepted: 19 January 2013
Published: 20 April 2014
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Authors |
| Haruya Mizutani | |
| Department of Mathematics, Graduate
School of Science Osaka University Toyonaka 560-0043 Japan |
Research Institute for Mathematical
Sciences Kyoto University Kyoto 606-8502 Japan |
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