Mathematical Surveys and Monographs 1990; 191 pp; hardcover Volume: 34 ISBN10: 0821815326 ISBN13: 9780821815328 List Price: US$96 Member Price: US$76.80 Order Code: SURV/34
 Inverse problems arise in many areas of mathematical physics, and applications are rapidly expanding to such areas as geophysics, chemistry, medicine, and engineering. The main theme of this book is uniqueness, stability, and existence of solutions of inverse problems for partial differential equations. Focusing primarily on the inverse problem of potential theory and closely related questions such as coefficient identification problems, this book will give readers an understanding of the results of a substantial part of the theory of inverse problems and of some of the new ideas and methods used. The author provides complete proofs of most general uniqueness theorems for the inverse problem of gravimetry, a detailed study of regularity properties (including examples of nonregular domains with regular potentials), counterexamples to uniqueness and uniqueness theorems, and a treatment of the theory of nonstationary problems. In addition, the book deals with the orthogonality method, formulates several important unsolved problems, and suggests certain technical means appropriate for further study; some numerical methods are also outlined. Requiring a background in the basics of differential equations and function theory, this book is directed at mathematicians specializing in partial differential equations and potential theory, as well as physicists, geophysicists, and engineers. Table of Contents  Preliminaries
 Results overlook
 Uniqueness theorems
 Singular points of the exterior potential
 Existence theory
 Parabolic problems
 Hyperbolic problems
