We present the solution of an inverse boundary value problem
for harmonic functions
arising in electrostatic imaging
through conformal mapping techniques.
The numerical method consists of two parts. In a first
step, by successive
approximations a nonlinear, nonlocal
ordinary differential equation is solved to determine the boundary values
of a holomorphic function on the outer boundary circle of an annulus.
Then in a second step an ill-posed Cauchy problem is solved to determine
the holomorphic function within the annulus.
We discuss a convergence result for the iteration procedure and
through numerical examples we illustrate the feasibility of
the method.
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