Summary: Zentralblatt MATH 1868 2008
c 2008 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag Berlin-Heidelberg
Ammari, Habib; Kang, Hyeonbae
Polarization and moment tensors. With applications to inverse problems
and effective medium theory. (English)
Applied Mathematical Sciences 162. New York, NY: Springer. x, 312 p. EUR 69.95/net;
SFR 122.00; $ 89.95; £ 54.00 (2007).
The present book deals with one of the most interesting topic in the Theory of Inverse
Problem: the detection of (small) inclusions in a (complex) medium and the localization
of their positions inside it, when a set of non-invasive pieces of information is available.
This means that measurements inside the body are to be avoided and that only boundary
measurements are allowed.
It is obvious to everyone the importance of such studies: the applications spread from
Biology and Medicine (e.g. research and localizations of tumors), to the determinations
of cracks in materials of interest in Technology.
From a mathematical point of view it is elliptic PDE's that play a basic role in this
theory, since the analysis of the previous questions is naturally concerned with stationary
problems. More exactly, transmission problems are the starting and the central point
of the investigations.