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

Kari Astala

ISBN 10: 0691137773 / ISBN 13: 9780691137773

Published by Princeton University Press, 2009

About this Item

Explores developments in the theory of planar quasiconformal mappings with a focus on the interactions with partial differential equations and nonlinear analysis. This book presents a modern approach to the classical theory and features applications across a spectrum of mathematics such as dynamical systems and singular integral operators. Series: Princeton Mathematical Series. Num Pages: 696 pages, 2 halftones. 17 line illus. BIC Classification: PBKJ. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 237 x 161 x 39. Weight in Grams: 1102. . 2008. First Edition. Hardcover. . . . .

Seller Inventory # V9780691137773

Bibliographic Details

• Title: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)
• Publisher: Princeton University Press
• Publication Date: 2009
• Language: English
• ISBN 10: 0691137773
• ISBN 13: 9780691137773
• Binding: Hardcover
• Edition: 1st Edition
• Condition: New

About this title

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.

About the Author

Kari Astala is the Finnish Academy Professor of Mathematics at the University of Helsinki. Tadeusz Iwaniec is the John Raymond French Distinguished Professor of Mathematics at Syracuse University. Gaven Martin is the Distinguished Professor of Mathematics at Massey University.