Discrete Calderón problem with partial data. (1st March 2023)

• Record Type: Journal Article
• Authors: Lecaros, Rodrigo; Ortega, Jaime H; Pérez, Ariel; De Teresa, Luz
• Is Part Of: Inverse problems. Volume 39:Number 3(2023)
• Publication Date: 2023-03-01
• Subjects: discrete inverse problem -- finite differences -- partial data -- discrete Carleman estimates -- stability estimate -- logarithmic stability estimate -- Calderón problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/acb0f8
• Languages: English
• ISSNs: 0266-5611

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.