UNIQUENESS AND STABILITY IN MULTIDIMENSIONAL INVERSE PROBLEMS

Recent results on uniqueness and stability of identification of coeffi cients and right sides of partial differential equations from overdete rmined boundary data are described. Elliptic, hyperbolic, and paraboli c equations and scattering theory are considered. Proofs are given or outlined whenever they contain a new and fruitful idea and are suffici ently short. This review is supposed to be quite comprehensive. In fac t, we do not cover only inverse spectral theory. Some interesting nume rical methods are mentioned, but numerics is also beyond the scope of this paper. A significant part is dedicated to so-called many boundary measurements (equations with given Dirichlet-to-Neumann map), but we also discuss results about single boundary measurements. An extensive bibliography contains basic papers in the field.