A stability analysis of the harmonic continuation

Abstract

We consider the Cauchy problem for harmonic functions outside some disc in the plane with the Cauchy data on an interval. We obtain simple formulae for singular values of the operator solving this Cauchy problem and explicit bounds on the difference between the exact and truncated operators. For a typical particular geometry we compute numerically these singular values and analyse their dependence on the size of the interval, on its distance to the disc, etc. As a consequence, we can tell how many parameters of the harmonic function (or of a source producing this function) can be found from the Cauchy data.