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Transactions of the American Mathematical Society

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An inverse boundary value problem for Schrödinger operators with vector potentials


Author: Zi Qi Sun
Journal: Trans. Amer. Math. Soc. 338 (1993), 953-969
MSC: Primary 35J10; Secondary 35R30, 47N50, 81Q05, 81V10
DOI: https://doi.org/10.1090/S0002-9947-1993-1179400-1
MathSciNet review: 1179400
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Abstract: We consider the Schrödinger operator for a magnetic potential $ \vec A$ and an electric potential $ q$, which are supported in a bounded domain in $ {\mathbb{R}^n}$ with $ n \geq 3$. We prove that knowledge of the Dirichlet to Neumann map associated to the Schrödinger operator determines the magnetic field $ \operatorname{rot}(\vec A)$ and the electric potential $ q$ simultaneously, provided $ \operatorname{rot}(\vec A)$ is small in the $ {L^\infty }$ topology.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1179400-1
Article copyright: © Copyright 1993 American Mathematical Society

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