Unique continuation for the Schrödinger equation with gradient term
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- by Youngwoo Koh and Ihyeok Seo PDF
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Abstract:
We obtain a unique continuation result for the differential inequality $| (i\partial _t +\Delta )u | \leq |Vu| + | W\cdot \nabla u |$ by establishing $L^2$ Carleman estimates. Here, $V$ is a scalar function and $W$ is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.References
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Additional Information
- Youngwoo Koh
- Affiliation: Department of Mathematics Education, Kongju National University, Kongju 32588, Republic of Korea
- MR Author ID: 910081
- Email: ywkoh@kongju.ac.kr
- Ihyeok Seo
- Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
- MR Author ID: 927090
- Email: ihseo@skku.edu
- Received by editor(s): June 9, 2017
- Received by editor(s) in revised form: August 28, 2017, and September 1, 2017
- Published electronically: February 1, 2018
- Additional Notes: The first author was supported by NRF Grant 2016R1D1A1B03932049 (Republic of Korea). The second author was supported by the NRF grant funded by the Korea government(MSIP) (No. 2017R1C1B5017496).
- Communicated by: Joachim Krieger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2555-2562
- MSC (2010): Primary 35B60, 35B45; Secondary 35Q40
- DOI: https://doi.org/10.1090/proc/13942
- MathSciNet review: 3778157