Nonlinear Functional Analysis and Its Applications

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 theheart ofthe problern under consideration and to concentrate on the basic ideas.

Preface; Preface to Second Corrected Printing; Translator's Preface; Introduction: Mathematics and Physics; APPLICATIONS IN MECHANICS: Basic Equations of Point Mechanics; Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles; APPLICATIONS IN ELASTICITY THEORY: Elastoplastic Wire; Basic Equations of Nonlinear Elasticity Theory; Monotone Potential Operators and a Class of Models with Nonlinear Hooke's Law, Duality and Plasticity, and Polyconvexity; Variational Inequalities and the Signorini Problem for Nonlinear Material; Bifurcation for Variational Inequalities; Pseudomonotone Operators, Bifurcation, and the von K rm n Plate Equations; Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis; APPLICATIONS IN THERMODYNAMICS: Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States; Statistical Physics; Continuation with Respect to a Parameter and a Radiation Problem of Carleman; APPLICATIONS IN HYDRODYNAMICS: Basic Equations of Hydrodynamics; Bifurcation and Permanent Gravitational Waves; Viscoud Fluids and the Navier-Stokes Equations; MANIFOLDS AND THEIR APPLICATIONS: Banach Manifolds; Classical Surface