An inverse problem in corrosion detection: stability estimates.

We consider the problem of detecting corrosion damage on an inaccessible part of a specimen. We adopt a model in which the corrosion damage is represented by an unknown boundary coefficient appearing in a third kind boundary value problem for Laplace's equation. The associated inverse problem consists in the determination of the unknown boundary coefficient from an overdetermined data on an accessible part of the boundary. In the present paper we are interested in the derivation of stability estimates for this inverse problem. We first prove a local Lipschitz stability estimate for an arbitrary smooth domain. Next, we establish a log-log stability estimate in the case of a rectangular domain. [ABSTRACT FROM AUTHOR]