Recovering All Coefficients in the Schr\"{o}dinger Equation With Finite Sets of Boundary Measurements
Year: 2025
Type: preprint
Abstract: We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by appropriately selecting a finite number of initial conditions and a fixed Dirichlet boundary condition, we may recover all the coefficients in a Lipschitz stable fashion from the corresponding finitely many boundary measurements made on a portion of the boundary. The proof is based on a direct approach, which was introduced in \cite{HIY2020}, to derive the stability estimate directly from the Carleman estimates without any cut-off procedure or compactness-uniqueness argument.
Source: arXiv (Cornell University)
Authors: Liu, Shitao, Pierrottet, Antonio
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979226379
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