Lipschitz stable determination of polygonal conductivity inclusions in a layered medium from the Dirichlet to Neumann map

TL;DR

This paper proves that the shape and location of polygonal conductivity inclusions within layered media can be stably determined from boundary measurements, with Lipschitz stability ensuring robustness against measurement errors.

Contribution

It extends previous results by establishing global Lipschitz stability for identifying polygonal inclusions in layered media using the Dirichlet to Neumann map.

Findings

Proves Lipschitz stability for polygonal inclusion identification

Extends previous stability results to layered media

Uses a distributed representation formula for the Gateaux derivative

Abstract

Using a distributed representation formula of the Gateaux derivative of the Dirichlet to Neumann map with respect to movements of a polygonal conductivity inclusion, [11], we extend the results obtained in [8] proving global Lipschitz stability for the determination of a polygonal conductivity inclusion embedded in a layered medium from knowledge of the Dirichlet to Neumann map.