Translations of Mathematical Monographs 1989; 362 pp; hardcover Volume: 73 ISBN10: 0821845268 ISBN13: 9780821845264 List Price: US$135 Member Price: US$108 Order Code: MMONO/73
 This book is intended for researchers and students concerned with questions in analysis and function theory. The author provides an exposition of the main results obtained in recent years by Soviet and other mathematicians in the theory of mappings with bounded distortion, an active direction in contemporary mathematics. The mathematical tools presented can be applied to a broad spectrum of problems that go beyond the context of the main topic of investigation. For a number of questions in the theory of partial differential equations and the theory of functions with generalized derivatives, this is the first time they have appeared in an internationally distributed monograph. Table of Contents  Introduction
 Some facts from the theory of functions of a real variable
 Functions with generalized derivatives
 Möbius transformations
 Definition of a mapping with bounded distortion
 Mappings with bounded distortion on Riemannian spaces
 Main facts in the theory of mappings with bounded distortion
 Estimates of the moduli of continuity and differentiability almost everywhere of mappings with bounded distortion
 Some facts about continuous mappings on \(R^n\)
 Conformal capacity
 The concept of the generalized differential of an exterior form
 Mappings with bounded distortion and elliptic differential equations
 Topological properties of mappings with bounded distortion
 Local structure of mappings with bounded distortion
 Characterization of mappings with bounded distortion by the property of quasiconformity
 Sequences of mappings with bounded distortion
 The set of branch points of a mapping with bounded distortion and locally homeomorphic mappings
 Extremal properties of mappings with bounded distortion
 Some further results
 Some results in the theory of functions of a real variable and the theory of partial differential equations
 Functions with bounded mean oscillation
 Harnack's inequality for quasilinear elliptic equations
 Theorems on semicontinuity and convergence with a functional for functionals of the calculus of variations
 Some properties of functions with generalized derivatives
 On the degree of a mapping
