Some links between 2D Laplace inverse problems and approximation in Hardy classes: constructive identification and stability properties

We consider the inverse problem of identifying a Robin coefficient on some part of the boundary of a smooth 2D domain from overdetermined data available on the other part of the boundary, for Laplace equation in the domain. Using tools from complex analysis and analytic functions theory, we provide a constructive and convergent identification scheme, together with a stability result for this inverse problem.