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 $\R^n$, $n\ge 3$, for the magnetic Schrödinger operator with $L^\infty$ 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.

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