We recover a nonlinear magnetic Schr\"odinger potential from measurement on an arbitrarily small open subset of the boundary on a compact Riemann surface. We assume that the magnetic potential satisfies suitable analytic properties, in which case the recovery can be obtained by a linearisation argument. The proof relies on the complex analytic methods introduced in [15].
Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential
The $L^p$ Carleman estimate and a partial data inverse problem
Inverse problem for a time-dependent Convection-diffusion equation in admissible geometries
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