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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 26, Issue 2

Issues

Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations

Ibtissem Ben Aïcha
  • Corresponding author
  • National Engineering School of Tunis, University of Tunis El Manar, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia
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/ Youssef Mejri
  • University of Aix-Marseille, 58 boulevard Charles Livon, 13284 Marseille, France; and Faculty of Sciences of Bizerte, University of de Carthage, 7021 Jarzouna Bizerte, Tunisia
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Published Online: 2017-09-12 | DOI: https://doi.org/10.1515/jiip-2017-0028

Abstract

We study the inverse problem of determining the magnetic field and the electric potential appearing in the magnetic Schrödinger equation from the knowledge of a finite number of lateral observations of the solution. We prove a Lipschitz stability estimate for both coefficients simultaneously by choosing the “initial” conditions suitably.

Keywords: Inverse problem; magnetic Schrödinger equation; stability estimate; finite number of partial Neumann measurements; Carleman estimate

MSC 2010: 35Mxx

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About the article

Received: 2017-03-24

Revised: 2017-06-01

Accepted: 2017-08-06

Published Online: 2017-09-12

Published in Print: 2018-04-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 2, Pages 201–209, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2017-0028.

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