Discrete Calderón problem with partial data

Abstract

Abstract In this work, we are interested in analyzing the well-known Calderón problem, which is an inverse boundary value problem of determining a coefficient function of an elliptic partial differential equation from the knowledge of the associated Dirichlet-to-Neumann map on the boundary of a domain. We consider the discrete version of the Calderon inverse problem with partial boundary data; in particular, we establish logarithmic stability estimates for the discrete Calderón problem, in dimension d ⩾ 3 , for the discrete H −r -norm on the boundary under suitable a priori bounds. The proof of our main result is based on a new discrete Carleman estimate for the discrete Laplacian operator with boundary observations.