Stability estimate for the discrete Calderon problem from partial data

Xiaomeng Zhao; Ganghua Yuan

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arXiv · 2405.06920

Stability estimate for the discrete Calderon problem from partial data

Xiaomeng Zhao·Ganghua Yuan

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Abstract

In this paper, we focus on the analysis of discrete versions of the Calderon problem with partial boundary data in dimension d >= 3. In particular, we establish logarithmic stability estimates for the discrete Calderon problem on an arbitrarily small portion of the boundary under suitable a priori bounds. For this end, we will use CGO solutions and derive a new discrete Carleman estimate and a key unique continuation estimate. Unlike the continuous case, we use a new strategy inspired by [32] to prove the key discrete unique continuation estimate by utilizing the new Carleman estimate with boundary observations for a discrete Laplace operator.

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Xiaomeng Zhao, Ganghua Yuan. 2024-05-11. Stability estimate for the discrete Calderon problem from partial data. https://arxiv.org/abs/2405.06920

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