Smoothness dependent stability in 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.

References in corpus (2)

• The stability for the Cauchy problem for elliptic equations
• Stable determination of surface impedance on a rough obstacle by far field data

Cited by in corpus (2)

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• Stability for an inverse flux and an inverse boundary coefficient problems