Variational Principles in Mathematical Physics, Geometry, and Economics
Variational Principles in Mathematical Physics, Geometry, and Economics
Vicenţiu D. Rădulescu, Institutul de Matematica 'Simion Stoilow' al Academiei Romane Bucuresti, Romania
Csaba Varga, Universitatea 'BabeÅŸ-Bolyai' Cluj-Napoca, Romania
£129.00
GBPThis 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.
- Rich with examples, exercises, figures and historical comments and includes a rich index and a comprehensive reference list
- Provides theoretical methods that allow the reader to develop research in basic fields connected with applications
- Contains new, previously unpublished material
Reviews & endorsements
'… an original attempt to rigorously introduce the principles of the calculus of variations underlying some interesting problems coming from various contexts: mathematical physics, geometry and optimization in economics. The main emphasis is placed on selected topics and their potential applications, since most of them have not been treated before in existing monographs.' Mathematical Reviews
'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
Product details
October 2014Adobe eBook Reader
9781107265974
0 pages
0kg
30 b/w illus. 45 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
