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The Beltrami Equation

A Geometric Approach

  • Vladimir Gutlyanskii
  • Vladimir Ryazanov
  • Uri Srebro
  • Eduard Yakubov

Part of the Developments in Mathematics book series (DEVM, volume 26)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 1-4
  3. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 5-45
  4. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 47-53
  5. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 55-76
  6. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 77-95
  7. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 97-128
  8. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 129-151
  9. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 153-169
  10. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 171-182
  11. Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 183-208
  12. Back Matter
    Pages 209-301

About this book

Introduction

The Beltrami Equation: A Geometric Approach will be particularly useful to many specialists in modern geometric analysis, quasiconformal mappings and extensions, beginning researchers, and graduate students with a year’s background in complex variables. This book covers the state-of-the art in the ongoing study of the Beltrami equation, the classical equation that has been studied for more than 100 years. Along with its rich history, the Beltrami equation plays a significant role in geometry, analysis, and physics.

 

The most important feature of this work concerns the unified geometric approach taken based on the modulus method that can be effectively applied to solving many problems in mathematical physics. Beautiful examples illustrate the relationship between mappings with bounded oscillation and those with finite oscillations.

 

Written by authors that are well-known specialists in this field, this monograph presents recent developments in the theory of Beltrami equations, studying a variety of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates, and boundary behavior of solutions to the Beltrami equations. It contains 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.

Keywords

Beltrami equation ordinary differential equations partial differential equations

Authors and affiliations

  • Vladimir Gutlyanskii
    • 1
  • Vladimir Ryazanov
    • 2
  • Uri Srebro
    • 3
  • Eduard Yakubov
    • 4
  1. 1.Institute of Applied Math. & Mechanics, Department of the Partial Differential ENational Academy of Sciences of UkraineDonetskUkraine
  2. 2.Institute of Applied Math. & Mechanics, Department of MathematicsNational Academy of Sciences of UkraineDonetskUkraine
  3. 3., Faculty of MathematicsTechnion Israel Institute of TechnologyHaifaIsrael
  4. 4., Faculty of SciencesH.I.T. - Holon Institute of TechnologyHolonIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-3191-6
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-3190-9
  • Online ISBN 978-1-4614-3191-6
  • Series Print ISSN 1389-2177
  • Buy this book on publisher's site