Inverse Dirichlet problem and conformal mapping

In this exposition we consider an inverse Dirichlet problem for harmonic functions that arises in the mathematical modelling of electrostatic imaging methods. In the first part we will survey the main ideas of some reconstruction procedures that have been employed for the numerical solution of this nonlinear and ill-posed inverse boundary value problem. In the second part we will outline a recently developed method that is based on conformal mapping techniques. By some numerical examples we will illustrate the feasibility of this new method.