Description: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)Author(s): Kari Astala, Tadeusz Iwaniec, Gaven Martin Format: Hardback Publisher: Princeton University Press, United States Imprint: Princeton University Press ISBN-13: 9780691137773, 978-0691137773 Synopsis 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.
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Book Title: Elliptic Partial Differential Equations and Quasiconformal Map...
Item Height: 235 mm
Item Width: 152 mm
Series: Princeton Mathematical Series
Author: Tadeusz Iwaniec, Kari Astala, Gaven Martin
Publication Name: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
Format: Hardcover
Language: English
Publisher: Princeton University Press
Subject: Mathematics
Publication Year: 2009
Type: Textbook
Item Weight: 1106 g
Number of Pages: 696 Pages
