Authors:
- Features a unified geometric approach based on the modulus method that is effectively applied to solving the Beltrami equation problems
- Presents recent developments in the theory of Beltrami equations, especially on degenerate and alternating Beltrami equations
- Discusses new concepts refining the analysis of problems related to the Beltrami equation, as well as applications of new research tools?
- Authors are well-known specialists in geometric function theory and elliptic differential equations
Part of the book series: Developments in Mathematics (DEVM, volume 26)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
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; especially those 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 behavior of solutions to the Beltrami equations. The monograph contains 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 book concerns 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 also gives 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.​
Authors and Affiliations
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Institute of Applied Math. & Mechanics, Department of the Partial Differential E, National Academy of Sciences of Ukraine, Donetsk, Ukraine
Vladimir Gutlyanskii
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Institute of Applied Math. & Mechanics, Department of Mathematics, National Academy of Sciences of Ukraine, Donetsk, Ukraine
Vladimir Ryazanov
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, Faculty of Mathematics, Technion Israel Institute of Technology, Haifa, Israel
Uri Srebro
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, Faculty of Sciences, H.I.T. - Holon Institute of Technology, Holon, Israel
Eduard Yakubov
Bibliographic Information
Book Title: The Beltrami Equation
Book Subtitle: A Geometric Approach
Authors: Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-3191-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-1-4614-3190-9Published: 20 April 2012
Softcover ISBN: 978-1-4899-9302-1Published: 08 May 2014
eBook ISBN: 978-1-4614-3191-6Published: 23 April 2012
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XIV, 302
Topics: Partial Differential Equations, Functions of a Complex Variable, Ordinary Differential Equations