Geometric Function Theory And Non Linear Analysis
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Geometric Function Theory And Non Linear Analysis
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Author : Tadeusz Iwaniec
language : en
Publisher: Clarendon Press
Release Date : 2001
Geometric Function Theory And Non Linear Analysis written by Tadeusz Iwaniec and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Language Arts & Disciplines categories.
This unique book explores the connections between the geometry of mappings and many important areas of modern mathematics such as Harmonic and non-linear Analysis, the theory of Partial Differential Equations, Conformal Geometry and Topology. Much of the book is new. It aims to provide students and researchers in many areas with a comprehensive and up to date account and an overview of the subject as a whole.
Convex Analysis And Nonlinear Geometric Elliptic Equations
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Author : Ilya J. Bakelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convex Analysis And Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Geometric Function Theory And Related Topics
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Author : Sudeb Mitra
language : en
Publisher: American Mathematical Society
Release Date : 2025-06-03
Geometric Function Theory And Related Topics written by Sudeb Mitra and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-03 with Mathematics categories.
This volume contains the proceedings of the 29th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, held August 21–25, 2023, at Pondicherry University, Puducherry, India. It covers a wide range of papers on complex analysis and provides a broad survey of the present state of research in various aspects of geometric function theory. The papers in this volume reflect the directions of research in different areas of finite- and infinite-dimensional complex analysis and also give the reader an idea of how these branches of complex analysis intersect with other areas of mathematics. They will be suitable for specialists as well as aspiring researchers who are interested in various areas of geometric function theory.
Semigroups In Geometrical Function Theory
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Author : D. Shoikhet
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-31
Semigroups In Geometrical Function Theory written by D. Shoikhet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-31 with Mathematics categories.
This manuscript provides an introduction to the generation theory of nonlinear one-parameter semigroups on a domain of the complex plane in the spirit of the Wolff-Denjoy and Hille-Yoshida theories. Special attention is given to evolution equations reproduced by holomorphic vector fields on the unit disk. A dynamic approach to the study of geometrical properties of univalent functions is emphasized. The book comprises six chapters. The preliminary chapter and chapter 1 give expositions to the theory of functions in the complex plane, and the iteration theory of holomorphic mappings according to Wolff and Denjoy, as well as to Julia and Caratheodory. Chapter 2 deals with elementary hyperbolic geometry on the unit disk, and fixed points of those mappings which are nonexpansive with respect to the Poincaré metric. Chapters 3 and 4 study local and global characteristics of holomorphic and hyperbolically monotone vector-fields, which yield a global description of asymptotic behavior of generated flows. Various boundary and interior flow invariance conditions for such vector-fields and their parametric representations are presented. Applications to univalent starlike and spirallike functions on the unit disk are given in Chapter 5. The approach described may also be useful for higher dimensions. Audience: The book will be of interest to graduate students and research specialists working in the fields of geometrical function theory, iteration theory, fixed point theory, semigroup theory, theory of composition operators and complex dynamical systems.
Geometrical Methods Of Nonlinear Analysis
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Author : Mark Aleksandrovich Krasnoselʹskiĭ
language : en
Publisher: Springer
Release Date : 1984
Geometrical Methods Of Nonlinear Analysis written by Mark Aleksandrovich Krasnoselʹskiĭ and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Non Linear Modeling And Analysis Of Solids And Structures
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Author : S. Krenk
language : en
Publisher: Cambridge University Press
Release Date : 2009-08-06
Non Linear Modeling And Analysis Of Solids And Structures written by S. Krenk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-06 with Mathematics categories.
Finite element analysis for non-linear solids and structure porblems.
Nonlinear Systems Analysis
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Author : M. Vidyasagar
language : en
Publisher: SIAM
Release Date : 2002-01-01
Nonlinear Systems Analysis written by M. Vidyasagar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
Fully Nonlinear Pdes In Real And Complex Geometry And Optics
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Author : Luca Capogna
language : en
Publisher: Springer
Release Date : 2013-10-07
Fully Nonlinear Pdes In Real And Complex Geometry And Optics written by Luca Capogna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-07 with Mathematics categories.
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.
Geometric Function Theory In One And Higher Dimensions
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Author : Ian Graham
language : en
Publisher: CRC Press
Release Date : 2003-03-18
Geometric Function Theory In One And Higher Dimensions written by Ian Graham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-18 with Mathematics categories.
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
Tensor Analysis And Nonlinear Tensor Functions
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Author : Yuriy I. Dimitrienko
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-11-30
Tensor Analysis And Nonlinear Tensor Functions written by Yuriy I. Dimitrienko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-30 with Mathematics categories.
Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.