This analysis reveals logarithmic stability in recovering potentials using the Neumann-to-Dirichlet map, highlighting advanced mathematical techniques.
In this paper, we study stability estimates for a Schr"odinger operator when recovering the potential in a bounded domain in Rⁿ with n ≥ 3, from measurements of a Neumann-to-Dirichlet map, with both inputs and outputs restricted to arbitrary open subsets of the boundary. Assuming that the potential is known in a neighborhood of the boundary, we obtain the logarithmic stability by a strategy of combining the CGO solution, a new Runge approximation and a new Carleman estimate.
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Zhao et al. (2025) studied this question.
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