The Dirichlet to Neumann map and applications

Introduction The subject of electrical impedance tomography has been extensively studied in the past few years. Substantial progress has been made in both the theoretical and applied aspects of the problem. We survey in this paper mathematical results pertaining to the case where the full Dirichlet to Neumann map (or voltage to current map) is known. We also discuss connections with other inverse problems such as inverse scattering and inverse spectral problems. For other closely related issues we refer to the article by Isakov in these proceedings.