For the logarithmic Schrödinger operator, the Dirichlet-to-Neumann map uniquely determines bounded potentials in arbitrary space dimension, and monotonicity gives a constructive reconstruction.
The Calder\'{o}n problem for nonlocal parabolic operators
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abstract
We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder\'on problems, respectively.
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2024 1verdicts
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The Calder\'on problem for the logarithmic Schr\"odinger equation
For the logarithmic Schrödinger operator, the Dirichlet-to-Neumann map uniquely determines bounded potentials in arbitrary space dimension, and monotonicity gives a constructive reconstruction.