Linearization of a free boundary problem in corrosion detection

We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part Gamma(1) subset of partial derivative Omega of the boundary of a bounded, planar domain Omega from one Cauchy data pair (u, partial derivative u/partial derivative v) of a harmonic potential u in Omega collected on an accessible boundary subset Gamma(A) subset of partial derivative Omega. We prove Frechet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem. (C) 2011 Elsevier Inc. All rights reserved.