Stability estimate for the discrete Calderón problem with partial data

KLAS, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 April 2025
Accepted: 13 March 2026

Abstract

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 [L. Robbiano, Asymptot. Anal. 10 (1995) 95-115] to prove the key discrete unique continuation estimate by utilizing the new Carleman estimate with boundary observations for a discrete Laplace operator.