An inverse problem in corrosion detection

We consider the problem of determining quantitative information about corrosion occurring on an inaccesible part of a specimen. The data for the problem consist of prescribed current flux and voltage measurements on an accessible part of the specimen boundary. The problem is modelled by Laplace's equation with an unknown term gamma in the boundary conditions. Our goal is recovering gamma from the data. We prove uniqueness under certain regularity assumptions and construct a regularized numerical method for obtaining approximate solutions to the problem. The numerical method, which is based on the assumption that the specimen is a thin plate, is tested in numerical experiments using synthetic data.