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 Γ I ⊂ ∂ Ω of the boundary of a bounded, planar domain Ω from one Cauchy data pair ( u , ∂ u / ∂ ν ) of a harmonic potential u in Ω collected on an accessible boundary subset Γ A ⊂ ∂ Ω . We prove Fréchet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem.