Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory [Hardcover]

Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the Potentials.- Near-Boundary Conductivity Inclusions.- Impedance Imaging of Conductivity Inclusions.- Effective Properties of Electrical Composites.- Transmission Problem for Elastostatics.- Elastic Moment Tensor.- Full Asymptotic Expansions of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.

From the reviews:

The main purpose of the book is to assess the influence of small-volume buried inclusions on measurements performed at the boundary of a domain of interest. & This self-contained book will serve as an excellent reference for any mathematician interested in the reconstruction of constitutive parameters in a differential equation from boundary measurements. (Guillaume Bal, Mathematical Reviews, Issue 2009 f)

The present book deals with one of the most interesting topics in the theory of inverse problems & . any chapter of the volume contains an interesting section devoted to Further results and open problems. & the volume is extremely well-written and organized, as well as (reasonably) self-contained, so that any reader with a good knowledge in elliptic PDEs and interest in inverse problems will enjoy it & . (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1220, 2011)

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors.

The main approach is based on modern layer potential techniques. Byls!