Variational principles in mathematical physics, geometry, and economics : qualitative analysis of nonlinear equations and unilateral problems
著者
書誌事項
Variational principles in mathematical physics, geometry, and economics : qualitative analysis of nonlinear equations and unilateral problems
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, [136]）
Cambridge University Press, 2010
- : hardback
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注記
Includes bibliographical references (p. [349]-360) and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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