Conditional stability estimation for an inverse boundary problem with non-smooth boundary in R-3

In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in R-3 by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipsc hitz continuous surface, we give a logarithmic conditional stability estima te in determining the part of boundary under reasonably a priori informatio n of an unknown part. The keys are the complex extension and estimates for a harmonic measure.