Nonlinear Functional Analysis and its Applications: IV: Applications to Mathematical Physics

✍ Scribed by Eberhard Zeidler (auth.)

• Publisher: Springer-Verlag New York
• Year: 1988
• Tongue: English
• Leaves: 1007
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Analysis; Theoretical, Mathematical and Computational Physics