Discrete Calderón problem with partial data. (1st March 2023) - Lecaros, Rodrigo; Ortega, Jaime H; Pérez, Ariel; De Teresa, Luz
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.