Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) /

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 compellin...

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Detalles Bibliográficos
Autores principales: Astala, Kari (Autor), Martin, Gaven (Autor), Iwaniec, Tadeusz (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, [2009]
Edición:Course book.
Colección:Book collections on Project MUSE.
Temas:
Quasiconformal mappings.
Mathematics.
Differential equations, Elliptic.
MATHEMATICS / Complex Analysis.
Mathematics > Complex Analysis.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Preface
  • Chapter 1. Introduction
  • Chapter 2. A Background In Conformal Geometry
  • Chapter 3. The Foundations Of Quasiconformal Mappings
  • Chapter 4. Complex Potentials
  • Chapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings
  • Chapter 6. Parameterizing General Linear Elliptic Systems
  • Chapter 7. The Concept Of Ellipticity
  • Chapter 8. Solving General Nonlinear First-Order Elliptic Systems
  • Chapter 9. Nonlinear Riemann Mapping Theorems
  • Chapter 10. Conformal Deformations And Beltrami Systems
  • Chapter 11. A Quasilinear Cauchy Problem
  • Chapter 12. Holomorphic Motions
  • Chapter 13. Higher Integrability
  • Chapter 14. Lp-Theory Of Beltrami Operators
  • Chapter 15. Schauder Estimates For Beltrami Operators
  • Chapter 16. Applications To Partial Differential Equations
  • Chapter 17. PDEs Not Of Divergence Type: Pucci'S Conjecture
  • Chapter 18. Quasiconformal Methods In Impedance Tomography: Calderón's Problem
  • Chapter 19. Integral Estimates For The Jacobian
  • Chapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case
  • Chapter 21. Aspects Of The Calculus Of Variations
  • Appendix: Elements Of Sobolev Theory And Function Spaces
  • Basic Notation
  • Bibliography
  • Index.

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