Stability for an inverse boundary problem of determining a part of a boundary

Abstract

In this paper, we discuss an inverse problem of determining a part of a boundary of a bounded domain in the plane. For the determination, we observe both Dirichlet and Neumann data on a subset of a known sub-boundary. We prove various conditional stability estimates according to a priori assumptions on the regularity of unknown sub-boundaries. Our results are: (i) in a general case the distance between two unknown sub-boundaries is conditionally estimated with double logarithmic rate under a priori assumption of C2-boundedness. (ii) we can improve stability rates through a single logarithmic rate up to Hölder continuity under the assumption that the sub-boundary is analytic.