Geometric Function Theory And Non Linear Analysis

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Geometric Function Theory and Non-linear Analysis

Tadeusz Iwaniec,Gaven Martin
Geometric Function Theory and Non linear Analysis Book PDF

Author : Tadeusz Iwaniec,Gaven Martin
Publisher : Clarendon Press
Page : 576 pages
File Size : 49,5 Mb
Release : 2001
Category : Language Arts & Disciplines
ISBN : 0198509294

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Geometric Function Theory and Non-linear Analysis by Tadeusz Iwaniec,Gaven Martin Pdf

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.

An Introduction to Nonlinear Analysis: Theory

Zdzisław Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou
An Introduction to Nonlinear Analysis Theory Book PDF

Author : Zdzisław Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou
Publisher : Springer Science & Business Media
Page : 708 pages
File Size : 48,8 Mb
Release : 2003
Category : Applied mathematics
ISBN : 0306473925

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An Introduction to Nonlinear Analysis: Theory by Zdzisław Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou Pdf

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

Nonlinear Theory of Generalized Functions

Michael Oberguggenberger,Michael Grosser,Michael Kunzinger,Gunther Hormann
Nonlinear Theory of Generalized Functions Book PDF

Author : Michael Oberguggenberger,Michael Grosser,Michael Kunzinger,Gunther Hormann
Publisher : Routledge
Page : 400 pages
File Size : 47,9 Mb
Release : 2022-02-28
Category : Mathematics
ISBN : 9781351428033

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Nonlinear Theory of Generalized Functions by Michael Oberguggenberger,Michael Grosser,Michael Kunzinger,Gunther Hormann Pdf

Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

Convex Analysis and Nonlinear Geometric Elliptic Equations

Ilya J. Bakelman
Convex Analysis and Nonlinear Geometric Elliptic Equations Book PDF

Author : Ilya J. Bakelman
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642698811

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Convex Analysis and Nonlinear Geometric Elliptic Equations by Ilya J. Bakelman Pdf

Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.

An Introduction to Nonlinear Analysis: Applications

Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou
An Introduction to Nonlinear Analysis Applications Book PDF

Author : Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 45,8 Mb
Release : 2003-01-31
Category : Computers
ISBN : 0306474565

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An Introduction to Nonlinear Analysis: Applications by Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou Pdf

This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

Geometric Analysis and Nonlinear Partial Differential Equations

Stefan Hildebrandt,Hermann Karcher
Geometric Analysis and Nonlinear Partial Differential Equations Book PDF

Author : Stefan Hildebrandt,Hermann Karcher
Publisher : Springer Science & Business Media
Page : 663 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556272

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Geometric Analysis and Nonlinear Partial Differential Equations by Stefan Hildebrandt,Hermann Karcher Pdf

This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Geometric Function Theory in One and Higher Dimensions

Ian Graham
Geometric Function Theory in One and Higher Dimensions Book PDF

Author : Ian Graham
Publisher : CRC Press
Page : 572 pages
File Size : 40,8 Mb
Release : 2003-03-18
Category : Mathematics
ISBN : 0203911628

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Geometric Function Theory in One and Higher Dimensions by Ian Graham Pdf

This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in

Nonlinear Analysis, Geometry and Applications

Diaraf Seck,Kinvi Kangni,Philibert Nang,Marie Salomon Sambou
Nonlinear Analysis Geometry and Applications Book PDF

Author : Diaraf Seck,Kinvi Kangni,Philibert Nang,Marie Salomon Sambou
Publisher : Springer Nature
Page : 462 pages
File Size : 54,8 Mb
Release : 2020-11-20
Category : Mathematics
ISBN : 9783030573362

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Nonlinear Analysis, Geometry and Applications by Diaraf Seck,Kinvi Kangni,Philibert Nang,Marie Salomon Sambou Pdf

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.

Semigroups in Geometrical Function Theory

D. Shoikhet
Semigroups in Geometrical Function Theory Book PDF

Author : D. Shoikhet
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 46,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401596329

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Semigroups in Geometrical Function Theory by D. Shoikhet Pdf

Historically, complex analysis and geometrical function theory have been inten sively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathemati cians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dy namical system: dx / dt + f ( x) = 0, where x is a variable describing the state of the system under study, and f is a vector function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the under lying space has been recently the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems (see, for example, [19, 13] and [29]). In a parallel development (and even earlier) the generation theory of one parameter semigroups of holomorphic mappings in en has been the topic of interest in the theory of Markov stochastic processes and, in particular, in the theory of branching processes (see, for example, [63, 127, 48] and [69]).

Geometric Nonlinear Functional Analysis

Yoav Benyamini,Joram Lindenstrauss
Geometric Nonlinear Functional Analysis Book PDF

Author : Yoav Benyamini,Joram Lindenstrauss
Publisher : American Mathematical Soc.
Page : 503 pages
File Size : 53,9 Mb
Release : 2000
Category : Nonlinear functional analysis
ISBN : 9780821808351

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Geometric Nonlinear Functional Analysis by Yoav Benyamini,Joram Lindenstrauss Pdf

A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.

Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Luca Capogna,Pengfei Guan,Cristian E. Gutiérrez,Annamaria Montanari
Fully Nonlinear PDEs in Real and Complex Geometry and Optics Book PDF

Author : Luca Capogna,Pengfei Guan,Cristian E. Gutiérrez,Annamaria Montanari
Publisher : Springer
Page : 210 pages
File Size : 47,6 Mb
Release : 2013-10-07
Category : Mathematics
ISBN : 9783319009421

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Fully Nonlinear PDEs in Real and Complex Geometry and Optics by Luca Capogna,Pengfei Guan,Cristian E. Gutiérrez,Annamaria Montanari Pdf

The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.

The Interaction of Analysis and Geometry

I͡Uriĭ Grigorʹevich Reshetni͡ak,Victor I. Burenkov,Tadeusz Iwaniec,Sergeĭ Konstantinovich Vodopʹi͡anov
The Interaction of Analysis and Geometry Book PDF

Author : I͡Uriĭ Grigorʹevich Reshetni͡ak,Victor I. Burenkov,Tadeusz Iwaniec,Sergeĭ Konstantinovich Vodopʹi͡anov
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 48,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840603

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The Interaction of Analysis and Geometry by I͡Uriĭ Grigorʹevich Reshetni͡ak,Victor I. Burenkov,Tadeusz Iwaniec,Sergeĭ Konstantinovich Vodopʹi͡anov Pdf

The papers in this volume are based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004). The topics include geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion (quasiregular mappings), nonlinear potential theory, Sobolev spaces, spaces with fractional and generalized smoothness, variational problems, and other modern trends in these areas. Most articles are related to Reshetnyak's original works and demonstrate the vitality of his fundamental contribution in some important fields of mathematics such as the geometry in the ""large"", quasiconformal analysis, Sobolev spaces, potential theory and variational calculus.

Nonlinear Analysis and Optimization

Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Nonlinear Analysis and Optimization Book PDF

Author : Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 52,5 Mb
Release : 2016-02-26
Category : Game theory, economics, social and behavioral sciences
ISBN : 9781470417369

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Nonlinear Analysis and Optimization by Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski Pdf

This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Geometric Function Theory in Several Complex Variables

Carl H. FitzGerald,Sheng Gong
Geometric Function Theory in Several Complex Variables Book PDF

Author : Carl H. FitzGerald,Sheng Gong
Publisher : World Scientific
Page : 360 pages
File Size : 46,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9812702504

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Geometric Function Theory in Several Complex Variables by Carl H. FitzGerald,Sheng Gong Pdf

The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

A Topological Introduction to Nonlinear Analysis

Robert F. Brown
A Topological Introduction to Nonlinear Analysis Book PDF

Author : Robert F. Brown
Publisher : Springer
Page : 240 pages
File Size : 43,9 Mb
Release : 2014-11-27
Category : Mathematics
ISBN : 9783319117942

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A Topological Introduction to Nonlinear Analysis by Robert F. Brown Pdf

This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)