This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
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Habib Ammari (born in June 1969) received the B.S., M.S., and Ph.D. degrees in mathematics from École Polytechnique Palaiseau in 1992, 1993, and 1995, respectively, and the Habilitation Degree from Université Pierre et Marie Curie (Paris 6), in 1999. He is currently Director of Research at the French Center of Scientific Research (CNRS). His current research interests include biomedical imaging, electrical impedance tomography, inverse problems, and electromagnetic modelling. He has contributed over 100 peer-reviewed articles and book chapters, authored four books and edited three others. He is serving as an editor of several mathematical journals. Habib Ammari has been invited to more than 30 international conferences. He produced 10 Ph.D. students and served as adviser for 10 post-docs.
This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
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