Conditional stability estimation for an inverse boundary problem with non-smooth boundary in $\mathcal {R}^3$

Abstract

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 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. © 2001 American Mathematical Society.