Inverse Boundary Value Problems

Abstract

To end this book we shall briefly indicate the application of ill-posed integral equations of the first kind and regularization techniques to inverse boundary value problems. In the ten years since the first edition of this book was written, the monograph [25] on inverse acoustic and electromagnetic scattering has appeared. Therefore, instead of considering an inverse obstacle scattering problem as in the first edition, in order to introduce the reader to current research in inverse boundary value problems we shall consider an inverse Dirichlet problem for the Laplace equation as a model problem. Of course, in a single chapter it is impossible to give a complete account of inverse boundary value problems. Hence we shall content ourselves with developing some of the main principles. For a detailed study of inverse boundary value problems, we refer to Colton and Kress [25] and Isakov [77].