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Space Mappings with Bounded Distortion
Yu. G. Reshetnyak
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Translations of Mathematical Monographs
1989; 362 pp; hardcover
Volume: 73
ISBN-10: 0-8218-4526-8
ISBN-13: 978-0-8218-4526-4
List Price: US$135
Member Price: US$108
Order Code: MMONO/73
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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
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