Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs

2024/02/07 by Martin Hanke, Hanke, Martin · 1 citation
Computer Science · Engineering · Mathematics · #35J25 #35R30 #65J22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.04651

openalex publication_date 2024/02/07 · openalex created_date 2024/02/09 · openalex updated_date 2026/07/28

Abstract

In 1996 Seo proved that two appropriate pairs of current and voltage data measured on the surface of a planar homogeneous object are sufficient to determine a conductive polygonal inclusion with known deviating conductivity. Here we show that the corresponding linearized forward map is injective, and from this we deduce Lipschitz stability of the solution of the original nonlinear inverse problem. We also treat the case of an insulating polygonal inclusion, in which case a single pair of Cauchy data is already sufficient for the same purpose.

Cited by

• A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems

Related

• Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements
• Lipschitz stable determination of polyhedral conductivity inclusions from local boundary measurements
• Lipschitz stable determination of polygonal conductivity inclusions in a\n layered medium from the Dirichlet to Neumann map
• Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement
• Uniqueness in the inverse conductivity problem for complex-valued\n Lipschitz conductivities in the plane