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E-book

Title The Beltrami equation : a geometric approach / Vladimir Gutlyanskii [and others]
Published New York, NY : Springer, ©2012

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Description 1 online resource (xiii, 301 pages)
Series Developments in mathematics, 1389-2177 ; v. 26
Developments in mathematics ; v. 26.
Contents Introduction -- Preliminaries -- The Classical Beltrami Equation [µ]∞<1 -- The Degenerate Case -- BMO- and FMO-Quasiconformal Mappings -- Ring Q-Homeomorphisms at Boundary Points -- Strong Ring Solutions of Beltrami Equations -- On the Dirichlet Problem for Beltrami Equations -- On the Beltrami Equations with Two Characteristics -- Alternating Beltrami Equation
Summary Annotation This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especiallythose concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behaviorof solutions to the Beltrami equations. The monographcontains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this bookconcerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools alsogives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book
Analysis Functions of complex variables
Differential Equations
Partial Differential Equations
Ordinary Differential Equations
wiskunde
mathematics
differentiaalvergelijkingen
Mathematics (General)
Wiskunde (algemeen)
Bibliography Includes bibliographical references and index
Notes English
Subject Conformal mapping.
Functions of complex variables.
Singularities (Mathematics)
Mathematics.
Mathematics
mathematics.
applied mathematics.
MATHEMATICS -- Complex Analysis.
Representación conforme
Singularidades (Matemáticas)
Matemáticas
Funciones de variables complejas
Mathematics
Conformal mapping
Functions of complex variables
Singularities (Mathematics)
Form Electronic book
Author Gutlyanskii, Vladimir
ISBN 9781461431916
1461431913
1461431905
9781461431909