Tadeusz Iwaniec's Books

Geometric Function Theory and Non-linear Analysis

By: Tadeusz Iwaniec,Gaven Martin

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Geometric Function Theory and Non-linear Analysis

By: Tadeusz Iwaniec,Gaven Martin

Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.

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Page Count

576

Publisher

Clarendon Press

Published Date

ISBN 10

0198509294

ISBN 13

9780198509295

The Beltrami Equation

By: Tadeusz Iwaniec,Gaven Martin

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The Beltrami Equation

By: Tadeusz Iwaniec,Gaven Martin

The measurable Riemann Mapping Theorem (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the state of the art as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.

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Page Count

110

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840452

ISBN 13

9780821840450

The Interaction of Analysis and Geometry

International School--Conference Analysis and Geometry, August 23-September 3, 2004, Novosibirsk, Russia

By: Victor I. Burenkov,Tadeusz Iwaniec,Sergeĭ Konstantinovich Vodopʹi︠a︡nov

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The Interaction of Analysis and Geometry

International School--Conference Analysis and Geometry, August 23-September 3, 2004, Novosibirsk, Russia

By: Victor I. Burenkov,Tadeusz Iwaniec,Sergeĭ Konstantinovich Vodopʹi︠a︡nov

Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory.

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Page Count

354

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840606

ISBN 13

9780821840603

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

By: Kari Astala,Tadeusz Iwaniec,Gaven Martin

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

By: Kari Astala,Tadeusz Iwaniec,Gaven Martin

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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Page Count

708

Publisher

Princeton University Press

Published Date

ISBN 10

0691137773

ISBN 13

9780691137773

$n$-Harmonic Mappings between Annuli

The Art of Integrating Free Lagrangians

By: Tadeusz Iwaniec,Jani Onninen

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$n$-Harmonic Mappings between Annuli

The Art of Integrating Free Lagrangians

By: Tadeusz Iwaniec,Jani Onninen

Iwaniec and Onninen (both mathematics, Syracuse U., US) address concrete questions regarding energy minimal deformations of annuli in Rn. One novelty of their approach is that they allow the mappings to slip freely along the boundaries of the domains, where it is most difficult to establish the existence, uniqueness, and invertibility properties of the extremal mappings. At the core of the matter, they say, is the underlying concept of free Lagrangians. After an introduction, they cover in turn principal radial n-harmonics, and the n-harmonic energy. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

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Page Count

120

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853570

ISBN 13

9780821853573

Potential Analysis of Stable Processes and its Extensions

By: Krzysztof Bogdan,Tomasz Byczkowski,Tadeusz Kulczycki,Michal Ryznar,Renming Song,Zoran Vondracek

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Potential Analysis of Stable Processes and its Extensions

By: Krzysztof Bogdan,Tomasz Byczkowski,Tadeusz Kulczycki,Michal Ryznar,Renming Song,Zoran Vondracek

Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.

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