Conformal mapping and inverse conductivity problem with one measurement

Laboratoire de Mathématiques Appliquées de Compiègne. Université de Technologie de Compiègne. Centre de Recherche de Royalieu 60200 Compiègne, France; marc.dambrine@dma.utc.fr

Received: 27 April 2005
Revised: 2 November 2005

Abstract

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series of numerical examples illustrating the performance of the method.