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Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane

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Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48

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Author : Kari Astala
language : en
Publisher: Princeton University Press
Release Date : 2009-01-18

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48 written by Kari Astala and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-18 with Mathematics categories.

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.

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48

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Author : Kari Astala
language : en
Publisher: Princeton University Press
Release Date : 2009-01-18

Lectures On Quasiconformal Mappings

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Author : Lars Valerian Ahlfors
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-07-14

Lectures On Quasiconformal Mappings written by Lars Valerian Ahlfors and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-14 with Mathematics categories.

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Harmonic Analysis Partial Differential Equations And Related Topics

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Author : Estela A. Gavosto
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Harmonic Analysis Partial Differential Equations And Related Topics written by Estela A. Gavosto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This collection of contributed articles comprises the scientific program of the fifth annual Prairie Analysis Seminar. All articles represent important current advances in the areas of partial differential equations, harmonic analysis, and Fourier analysis. A range of interrelated topics is presented, with articles concerning Painleve removability, pseudodifferential operators, $A p$ weights, nonlinear Schrodinger equations, singular integrals, the wave equation, the Benjamin-Ono equation, quasi-geostrophic equations, quasiconformal mappings, integral inclusions, Bellman function methods, weighted gradient estimates, Hankel operators, and dynamic optimization problems. Most importantly, the articles illustrate the fruitful interaction between harmonic analysis, Fourier analysis, and partial differential equations, and illustrate the successful application of techniques and ideas from each of these areas to the others.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Generalized Analytic Functions

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Author : I. N. Vekua
language : en
Publisher: Elsevier
Release Date : 2014-07-17

Generalized Analytic Functions written by I. N. Vekua and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-17 with Mathematics categories.

Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and research workers.

Conformally Invariant Metrics And Quasiconformal Mappings

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Author : Parisa Hariri
language : en
Publisher: Springer Nature
Release Date : 2020-04-11

Conformally Invariant Metrics And Quasiconformal Mappings written by Parisa Hariri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-11 with Mathematics categories.

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

Quasiconformal Space Mappings

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Author : Matti Vuorinen
language : en
Publisher: Springer
Release Date : 2006-11-14

Quasiconformal Space Mappings written by Matti Vuorinen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of quasiregular mappings.- O. Martio: Partial differential equations and quasiregular mappings.- Yu.G. Reshetnyak: On functional classes invariant relative to homothetics.- S. Rickman: Picard's theorem and defect relation for quasiconformal mappings.- U. Srebro: Topological properties of quasiregular mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.

The Ubiquitous Quasidisk

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Author : Frederick W. Gehring
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

The Ubiquitous Quasidisk written by Frederick W. Gehring and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This book focuses on gathering the numerous properties and many different connections with various topics in geometric function theory that quasidisks possess. A quasidisk is the image of a disk under a quasiconformal mapping of the Riemann sphere. In 1981 Frederick W. Gehring gave a short course of six lectures on this topic in Montreal and his lecture notes ``Characteristic Properties of Quasidisks'' were published by the University Press of the University of Montreal. The notes became quite popular and within the next decade the number of characterizing properties of quasidisks and their ramifications increased tremendously. In the late 1990s Gehring and Hag decided to write an expanded version of the Montreal notes. At three times the size of the original notes, it turned into much more than just an extended version. New topics include two-sided criteria. The text will be a valuable resource for current and future researchers in various branches of analysis and geometry, and with its clear and elegant exposition the book can also serve as a text for a graduate course on selected topics in function theory. Frederick W. Gehring (1925-2012) was a leading figure in the theory of quasiconformal mappings for over fifty years. He received numerous awards and shared his passion for mathematics generously by mentoring twenty-nine Ph.D. students and more than forty postdoctoral fellows. Kari Hag received her Ph.D. under Gehring's direction in 1972 and worked with him on the present text for more than a decade.

Elliptic Partial Differential Equations Of Second Order

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Author : David Gilbarg
language : en
Publisher: Springer
Release Date : 2015-03-30

Elliptic Partial Differential Equations Of Second Order written by David Gilbarg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-30 with Mathematics categories.

From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 " ... as should be clear from the previous discussion, this book is a bibliographical monument to the theory of both theoretical and applied PDEs that has not acquired any flaws due to its age. On the contrary, it remains a crucial and essential tool for the active research in the field. In a few words, in my modest opinion, “. . . this book contains the essential background that a researcher in elliptic PDEs should possess the day s/he gets a permanent academic position. . . .” SIAM Newsletter

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane

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