Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

TL;DR

This paper establishes a Lipschitz stability estimate for the electrostatic inverse boundary value problem with piecewise linear conductivities, enhancing the understanding of how boundary measurements determine internal conductivities.

Contribution

The paper proves a Lipschitz stability estimate for piecewise linear conductivities in EIT, providing a quantitative stability result for the inverse problem.

Findings

Lipschitz stability estimate established for piecewise linear conductivities

Quantitative relation between boundary data and internal conductivities

Improved understanding of stability in electrostatic inverse problems

Abstract

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true.