Inverse Problems for Partial Differential Equations

Inverse Problems.- Ill-Posed Problems and Regularization.- Uniqueness and Stability in the Cauchy Problem.- Elliptic Equations: Single Boundary Measurements.- Elliptic Equations: Many Boundary Measurements.- Scattering Problems.- Integral Geometry and Tomography.- Hyperbolic Problems.- Inverse parabolic problems.- Some Numerical Methods.

Since the first publication of this book, the rapidly progressing field of inverse problems witnessed changes and new developments. This book reflects these changes and describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations.
Currently, there are hundreds of publications containing new and interesting results on the topic of inverse problems. This book successfully collects and presents many of them in a readable and informative form. This second edition is considerably expanded and some concepts (like pseudo-convexity) or proofs are simplified. New material is added to reflect recent progress in theory of inverse problems.
This useful and stimulating material is intended for a reader with a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis. It formulates basic inverse problems, discusses regularization, gives a short review of uniqueness in the Cauchy problem, and includes several exercises. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. Parts of the book in a preliminary form have been presented as graduate courses at a number of universities.