This work deals with a non linear inverse problem of reconstructingan unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type,by using boundary measurements. The problem is turned into an optimal shape design one, by constructinga Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary.Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u 0, and not on its Lagrangian derivative u1(θ).
