Stability of the solution of an inverse problem for Laplace's equation in a thin strip

Assume that a Robin boundary condition models the presence of defects in the thermal (or electric) insulation of the top side of the open rectangular domain $\Omega$. The temperature fulfills Laplace's equation. Here we study the inverse problem of recovering the heat exchange coefficient $\gamma$ in the Robin condition, from the knowledge of a Cauchy data set on the bottom side of $\Omega$. We derive logaritmic stability estimates under suitable apriori informtation about \gamma and discuss the relation between the stability of solutions and thickness of domain.