Smoothness dependent stability in corrosion detection

TL;DR

This paper investigates the stability of detecting corrosion boundaries in conductors using electrostatic measurements, showing improved stability results with smoother boundary assumptions.

Contribution

It establishes a global log-log stability for Lipschitz boundaries and improves it to a global log stability for $C^{1,1}$-smooth boundaries in corrosion detection.

Findings

Global log-log stability for Lipschitz boundaries

Enhanced global log stability for $C^{1,1}$-smooth boundaries

Quantitative stability estimates in electrostatic corrosion detection

Abstract

We consider the stability issue for the determination of a linear corrosion in a conductor by a single electrostatic measurement. We established a global log-log type stability when the corroded boundary is simply Lipschitz. We also improve such a result obtaining a global log stability by assuming that the damaged boundary is $C^{1,1}$-smooth.