| Affiliation: | Department of Mathematics, Fudan University, Shanghai 200433, China & Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376-8515, Japan ; Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong ; Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan |
| Abstract: | ![]()
In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in  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. |
