Abstract
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 Ω ⊂ R 2. The temperature (or electrostatic potential, respectively) in Ω satisfies the Laplace's equation. Here we study the inverse problem of recovering the heat exchange coefficient γ in the Robin condition from the knowledge of a Cauchy data set on the bottom side of Ω. We derive logarithmic stability estimates under suitable a priori informations about γ, and discuss the relation between stability of the solution and thickness of the domain.
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