Nonlinear Functional Analysis and its Applications / Applications to Mathematical Physics

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 should be accessible to the non-specialist. It attempts to combine classical and modern ideas and to build a bridge between the language and thoughts of physicists and mathematicians. This corrected printing is fully revised and contains a new section of additional references along with many exercises. Topics covered in this volume 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.