Stability estimate for the discrete Calderón problem with partial data

In this paper, we focus on the analysis of discrete versions of the Calderón problem with partial boundary data in dimension d≥ 3. In particular, we establish logarithmic stability estimates for the discrete Calderón 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 novel unique continuation estimate. Unlike the continuum case, we use a new strategy inspired by [35] to prove the key discrete unique continuation estimate by utilizing the new Carleman estimate with boundary observations for a discrete Laplace operator.