Variational Principles in Mathematical Physics, Geometry, and Economics

A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

The informal approach of this introductory text stresses naturality and functoriality from the beginning. Based on the authors' original work, it provides a comprehensive overview of the field suitable for graduate students entering research. Its extensive bibliography, glossary, and index make this book a valuable reference.This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and exercises suitable for graduate students entering research. The method of presentation will appeal to readers with diverse backgrounds in functional analysis, differential geometry and partial differential equations. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. Since much of the material has a strong geometric flavor, the authors have supplemented the text with figures to illustrate the abstract concepts. Its extensive reference list and index also make this a valuable resource for researchers working in a variety of fields who are interested in partial differential equations and functional analysis.