Determining a magnetic Schrödinger operator with a continuous magnetic potential from boundary measurements
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Determining a magnetic Schrödinger operator with a continuous magnetic potential from boundary measurements

  • Author(s): Krupchyk, Katsiaryna
  • Uhlmann, Gunther
  • et al.
Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schr\"odinger operator with a gain of two derivatives.

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