Carleman estimate for the Schrödinger equation and application to magnetic inverse problems

In this paper, we prove Lipschitz stable determination of the complex-valued electric potential and the direction of the magnetic field appearing in the dynamic Schrödinger equation with static coefficients, by finitely many partial boundary measurements of the solution. This is by means of the Bukhgeim–Klibanov method, based on an appropriate Carleman estimate. Since the time symmetrization of the static magnetic Schrödinger equation around t=0 is not possible, we preliminarily establish a Carleman inequality specifically designed for this problem. © 2019 Elsevier Inc.

Authors
Huang X.1 , Kian Y.2 , Soccorsi É.2 , Yamamoto M. 1, 3
Publisher
Academic Press Inc.
Number of issue
1
Language
English
Pages
116-142
Status
Published
Volume
474
Year
2019
Organizations
  • 1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153, Japan
  • 2 Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Carleman estimate; Magnetic Schrödinger equation; Multidimensional inverse coefficient problem
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38619/