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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