Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane
eBook - PDF

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

  1. 696 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

About this book

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings.


The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane by Kari Astala,Tadeusz Iwaniec,Gaven Martin in PDF and/or ePUB format, as well as other popular books in Mathematics & Complex Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Contents
  2. Preface
  3. 1 Introduction
  4. 2 A Background in Conformal Geometry
  5. 3 The Foundations of Quasiconformal Mappings
  6. 4 Complex Potentials
  7. 5 The Measurable Riemann Mapping Theorem: The Existence Theory of Quasiconformal Mappings
  8. 6 Parameterizing General Linear Elliptic Systems
  9. 7 The Concept of Ellipticity
  10. 8 Solving General Nonlinear First-Order Elliptic Systems
  11. 9 Nonlinear Riemann Mapping Theorems
  12. 10 Conformal Deformations and Beltrami Systems
  13. 11 A Quasilinear Cauchy Problem
  14. 12 Holomorphic Motions
  15. 13 Higher Integrability
  16. 14 L[sup(p)]-Theory of Beltrami Operators
  17. 15 Schauder Estimates for Beltrami Operators
  18. 16 Applications to Partial Diffierential Equations
  19. 17 PDEs Not of Divergence Type: Pucci's Conjecture
  20. 18 Quasiconformal Methods in Impedance Tomography: Calderón's Problem
  21. 19 Integral Estimates for the Jacobian
  22. 20 Solving the Beltrami Equation: Degenerate Elliptic Case
  23. 21 Aspects of the Calculus of Variations
  24. Appendix: Elements of Sobolev Theory and Function Spaces
  25. Basic Notation
  26. Bibliography
  27. Index