Lipschitz stable determination of polyhedral conductivity inclusions from local boundary measurements

TL;DR

This paper establishes a Lipschitz stability result for identifying polyhedral conductivity inclusions inside a medium using boundary measurements, extending previous 2D results to 3D.

Contribution

It provides the first global Lipschitz stability proof for 3D polyhedral inclusions from boundary data, advancing the mathematical understanding of inverse conductivity problems.

Findings

Proves Lipschitz stability for 3D polyhedral inclusions

Extends 2D results to three dimensions

Enhances the theoretical framework for inverse boundary value problems

Abstract

We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [18] and [19] in the two-dimensional case to the three-dimensional setting.