Main subject categories: • Nonlinear functional analysis • Applications to mathematical physics"The main concern in all scientific work must be the human being himself." This, one should never forget among all those diagrams and equations. ‒ Albert EinsteinThis volume is part of a comprehensive presentation of nonlinear functional analysis, the basic content of which has been outlined in the Preface of Part I. A Table of Contents for all five volumes may also be found in Part I.The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Part IV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? What typical applications are there? Special emphasis is placed on motivation.Part IV contain applications to mathematical present physics. Our goals are the following: (i) A detailed motivation of the basic equations in important disciplines of theoretical physics. (ii) A discussion of particular problems which have played a significant role in the development of physics, and through which important mathematical and physical insight may be gained. (iii) A combination of classical and modern ideas. (iv) An attempt to build a bridge between the language and thoughts of physicists and mathematicians. We shall always try to advance as soon as possible to the heart of the problem under consideration and to concentrate on the basic ideas.The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. Front Matter....Pages i-xxiii Introduction....Pages 1-6 Front Matter....Pages 7-7 Basic Equations of Point Mechanics....Pages 9-97 Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles....Pages 98-141 Front Matter....Pages 143-144 Elastoplastic Wire....Pages 145-157 Basic Equations of Nonlinear Elasticity Theory....Pages 158-232 Monotone Potential Operators and a Class of Models with Nonlinear Hooke’s Law, Duality and Plasticity, and Polyconvexity....Pages 233-295 Variational Inequalities and the Signorini Problem for Nonlinear Material....Pages 296-302 Bifurcation for Variational Inequalities....Pages 303-321 Pseudomonotone Operators, Bifurcation, and the von Kármán Plate Equations....Pages 322-347 Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis....Pages 348-361 Front Matter....Pages 363-367 Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States....Pages 369-395 Statistical Physics....Pages 396-421 Continuation with Respect to a Parameter and a Radiation Problem of Carleman....Pages 422-430 Front Matter....Pages 431-431 Basic Equations of Hydrodynamics....Pages 433-447 Bifurcation and Permanent Gravitational Waves....Pages 448-478 Viscous Fluids and the Navier—Stokes Equations....Pages 479-526 Front Matter....Pages 527-527 Banach Manifolds....Pages 529-608 Classical Surface Theory, the Theorema Egregium of Gauss, and Differential Geometry on Manifolds....Pages 609-693 Special Theory of Relativity....Pages 694-729 General Theory of Relativity....Pages 730-793 Front Matter....Pages 527-527 Simplicial Methods, Fixed-Point Theory, and Mathematical Economics....Pages 794-816 Homotopy Methods and One-Dimensional Manifolds....Pages 817-839 Dynamical Stability and Bifurcation in B-Spaces....Pages 840-882 Back Matter....Pages 883-993 The main concern in all scientific work must be the human being himsel[ This, one should never forget among all those diagrams and equations. Albert Einstein This volume is part of a comprehensive presentation of nonlinear functional analysis, the basic content of which has been outlined in the Preface of Part I. A Table of Contents for all five volumes may also be found in Part I. The Part IV and the following Part V contain applications to mathematical present physics. Our goals are the following: (i) A detailed motivation of the basic equations in important disciplines of theoretical physics. (ii) A discussion of particular problems which have played a significant role in the development of physics, and through which important mathe matical and physical insight may be gained. (iii) A combination of classical and modern ideas. (iv) An attempt to build a bridge between the language and thoughts of physicists and mathematicians. Weshall always try to advance as soon as possible to the heart ofthe problern under consideration and to concentrate on the basic ideas. The main concern in all scientific work must be the human being himsel[This, one should never forget among all those diagrams and equations. Albert Einstein This volume is part of a comprehensive presentation of nonlinear functional analysis, the basic content of which has been outlined in the Preface of Part I.A Table of Contents for all five volumes may also be found in Part I. The Part IV and the following Part V contain applications to mathematical present physics. Our goals are the following: (i) A detailed motivation of the basic equations in important disciplines of theoretical physics. (ii) A discussion of particular problems which have played a significant role in the development of physics, and through which important matheƯ matical and physical insight may be gained. (iii) A combination of classical and modern ideas. (iv) An attempt to build a bridge between the language and thoughts of physicists and mathematicians. Weshall always try to advance as soon as possible to the heart ofthe problern under consideration and to concentrate on the basic ideas This Is The Fourth Of A Five-volume Exposition Of The Main Principles Of Nonlinear Functional Analysis And Its Applications To The Natural Sciences, Economics, And Numerical Analysis. The Presentation Is Self-contained And Accessible To The Nonspecialist. Topics Covered In This Volume Include Applications To Mechanics, Elasticity, Plasticity, Hydrodynamics, Thermodynamics, Stastical Physics, And Special And General Relativity Including Cosmology. The Book Contains A Detailed Physical Motivation Of The Relevant Basic Equations And A Discussion Of Particular Problems Which Have Played A Significant Role In The Development Of Physics And Through Which Important Mathematical And Physical Insight May Be Gained. An Attempt Is Made To Combine Classical And Modern Ideas And To Build A Bridge Between The Language And Thoughts Of Physicists And Mathematicians. Many Exercises And A Comprehensive Bibliography Complement The Text. This Corrected Printing Contains Many Revisions As Well As A List Of New And Recent References. By Eberhard Zeidler.
this Is The Fourth Of A Five-volume Exposition Of The Main Principles Of Nonlinear Functional Analysis And Its Applications To The Natural Sciences, Economics, And Numerical Analysis. The Presentation Is Self-contained And Accessible To The Nonspecialist. Topics Covered In This Volume Include Applications To Mechanics, Elasticity, Plasticity, Hydrodynamics, Thermodynamics, Stastical Physics, And Special And General Relativity Including Cosmology. The Book Contains A Detailed Physical Motivation Of The Relevant Basic Equations And A Discussion Of Particular Problems Which Have Played A Significant Role In The Development Of Physics And Through Which Important Mathematical And Physical Insight May Be Gained. An Attempt Is Made To Combine Classical And Modern Ideas And To Build A Bridge Between The Language And Thoughts Of Physicists And Mathematicians. Many Exercises And A Comprehensive Bibliography Complement The Text. This Corrected Printing Contains Many Revisions As Well As A List Of New And Recent References.
The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text. A contemporary natural scientist to a mathematician Numerous questions in physics, chemistry, biology, and economics lead to nonlinear problems; diffusion processes in physics, chemistry, and biology; processes with entropy production, and self-organization of systems in physics, chemistry, and biology; This text covers nonlinear functional analysis and its applications, with a specific emphasis on nonlinear monotone operators.
