In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in R³ by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipschitz continuous surface, we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part. The keys are the complex extension and estimates for a harmonic measure.
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Cheng et al. (2001) studied this question.