We consider a boundary identification problem arising in nondestructive testing of
materials. The problem is to recover a part ΓI ⊂ ∂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 ΓA ⊂ ∂Ω. We prove Fréchet differentiability of a suitably
defined forward map, and discuss local uniqueness and Lipschitz stability results for the
linearized problem.
