Preface
This volume consists of the Proceedings of the Workshop on Inverse Problems
and Applications organized by the Istituto Nazionale di Alta Matematica Francesco
Severi (INdAM), which was held in Cortona, Italy, June 3-9, 2002 and of the
Special Session Inverse Boundary Problems and Applications held at the First Joint
Meeting of the American Mathematical Society and of the Unione Matematica
Italiana, Pisa, Italy, June 12-16, 2002.
One of the main objectives of the workshops was to interchange ideas and
encourage interaction between American and Italian scientists interested in Inverse
Problems.
Inverse Problems arise in practical situations such as medical imaging, explo-
ration geophysics, and non-destructive evaluation where measurements made in the
exterior of a body are used to deduce properties of the hidden interior. A large
class of inverse problems arise from a physical situation modeled by a partial dif-
ferential equation. The inverse problem is to determine some coefficients of the
equation given some information about the solutions. Analysis of such problems
brings together diverse areas of mathematics such as complex analysis, differen-
tial geometry, harmonic analysis, integral geometry, microlocal analysis, numerical
analysis, optimization, partial differential equations, probability etc. and is a fertile
area for interaction between pure and applied mathematics. This interplay is well
represented during these proceedings where several theoretical and applied aspects
of inverse problems are considered.
This book includes articles on a broad range of inverse problems including the
inverse conductivity problem, inverse problems for Maxwell's equations, time rever-
sal mirrors, ultrasound using elastic pressure waves, inverse problems arising in the
environment, inverse scattering for the three body problem and optical tomography.
This volume also include several articles on unique continuation, a closely related
subject to inverse problems, as well as the study of propagation of singularities for
hyperbolic equations in anisotropic media.
We thank IN dAM for the support of the Cortona Workshop, we also acknowl-
edge additional support from the Ministero dell'Istruzione, dell'Universita e della
Ricerca (National Research Project 2000 Inverse problems in medical imaging) and
from the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Ap-
plicazioni of INdAM (Progetto di Ricerca e Formazione 2001 Problemi Inversi).
Furthermore we thank all the participants for their contributions to these suc-
cessful and enjoyable workshops. We are grateful also to the referees for their
prompt and attentive reports.
The Editors
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