We are concerned with a problem arising in corrosion detection. We consider the stability issue for the inverse problem of determining a Robin coefficient on the inaccessible portion of the boundary by the electrostatic measurements performed on the accessible one. We provide a Lipschitz stability estimate under the further a priori assumption of a piecewise constant Robin coefficient. Furthermore, we prove that the Lipschitz constant of the above-mentioned estimate behaves exponentially with respect to the number of the portions considered.

We consider the inverse boundary value problem of determining the potential q in the equation ∆u + qu = 0 in Ω ⊂ R n , from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n ≥ 3 for potentials that are piecewise linear on a given partition of Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation ∆u + k 2 c −2 u = 0 at fixed frequency k.

We deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one.

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain ⊂ R^n and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true