Variational Principles in Mathematical Physics, Geometry, and Economics
Qualitative Analysis of Nonlinear Equations and Unilateral Problems

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

Alexandru Kristály (Author), Vicen?iu D. R?dulescu (Author), Csaba Varga (Author)

9780521117821, Cambridge University Press

Hardback, published 19 August 2010

386 pages, 30 b/w illus. 45 exercises
23.6 x 16.3 x 2.8 cm, 0.72 kg

'The interesting method of presentation of the book, with extensive reference list and index, make me believe that the book will be appreciated by mathematicians, engineers, economists, physicists, and all scientists interested in variational methods and in their applications.' Zentralblatt MATH

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.

Foreword Jean Mawhin
Preface
Part I. Variational Principles in Mathematical Physics: 1. Variational principles
2. Variational inequalities
3. Nonlinear eigenvalue problems
4. Elliptic systems of gradient type
5. Systems with arbitrary growth nonlinearities
6. Scalar field systems
7. Competition phenomena in Dirichlet problems
8. Problems to Part I
Part II. Variational Principles in Geometry: 9. Sublinear problems on Riemannian manifolds
10. Asymptotically critical problems on spheres
11. Equations with critical exponent
12. Problems to Part II
Part III. Variational Principles in Economics: 13. Mathematical preliminaries
14. Minimization of cost-functions on manifolds
15. Best approximation problems on manifolds
16. A variational approach to Nash equilibria
17. Problems to Part III
Appendix A. Elements of convex analysis
Appendix B. Function spaces
Appendix C. Category and genus
Appendix D. Clarke and Degiovanni gradients
Appendix E. Elements of set-valued analysis
References
Index.

Subject Areas: Mathematical physics [PHU], Applied mathematics [PBW], Differential calculus & equations [PBKJ]