Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in R n , n ≥ 3 , for the magnetic Schrödinger operator with L ∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carle...

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Bibliographic Details
Published in:Communications in mathematical physics 2014-05, Vol.327 (3), p.993-1009
Main Authors: Krupchyk, Katsiaryna, Uhlmann, Gunther
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in R n , n ≥ 3 , for the magnetic Schrödinger operator with L ∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-1942-z