Format:
Online-Ressource (696 p.)
Edition:
Online-Ausg.
ISBN:
9780691137773
Series Statement:
Princeton Mathematical Series v.v. 48
Content:
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
Note:
Description based upon print version of record
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Contents; Preface; 1 Introduction; 2 A Background in Conformal Geometry; 3 The Foundations of Quasiconformal Mappings; 4 Complex Potentials; 5 The Measurable Riemann Mapping Theorem: The Existence Theory of Quasiconformal Mappings; 6 Parameterizing General Linear Elliptic Systems; 7 The Concept of Ellipticity; 8 Solving General Nonlinear First-Order Elliptic Systems; 9 Nonlinear Riemann Mapping Theorems; 10 Conformal Deformations and Beltrami Systems; 11 A Quasilinear Cauchy Problem; 12 Holomorphic Motions; 13 Higher Integrability; 14 L[sup(p)]-Theory of Beltrami Operators
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15 Schauder Estimates for Beltrami Operators16 Applications to Partial Diffierential Equations; 17 PDEs Not of Divergence Type: Pucci's Conjecture; 18 Quasiconformal Methods in Impedance Tomography: Calderón's Problem; 19 Integral Estimates for the Jacobian; 20 Solving the Beltrami Equation: Degenerate Elliptic Case; 21 Aspects of the Calculus of Variations; Appendix: Elements of Sobolev Theory and Function Spaces; Basic Notation; Bibliography; Index;
Additional Edition:
ISBN 9781400830114
Additional Edition:
Erscheint auch als Druck-Ausgabe Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)
Additional Edition:
Erscheint auch als Druck-Ausgabe Astala, Kari, 1953 - Elliptic partial differential equations and quasiconformal mappings in the plane Princeton, NJ : Princeton University Press, 2009 ISBN 9780691137773
Additional Edition:
ISBN 0691137773
Language:
English
Keywords:
Electronic books
