Variational Principles in Mathematical Physics, Geometry, and Economics

Qualitative Analysis of Nonlinear Equations and Unilateral Problems
Erscheinungsjahr 2011
ISBN: 978-0-521-11782-1
Verlag: Cambridge University Press

Buch, Englisch, Band 136, 370 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 743 g

Reihe: Encyclopedia of Mathematics and its Applications

• 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• Contains new, previously unpublished material
This comprehensive introduction to the calculus of variations and ist 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. Ist 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.

Autoren/Hrsg.

Kristály, Alexandru

Rădulescu, Vicenţiu D.

Varga, Csaba

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Kristály, Alexandru
Alexandru Kristály is Associate Professor in the Department of Economics at the University of Babeş-Bolyai in Cluj-Napoca, Romania.

Varga, Csaba
Csaba Gyorgy Varga is Professor in the Department of Mathematics at the University of Babeş-Bolyai in Cluj-Napoca, Romania.

Rădulescu, Vicenţiu D.
Vicenţiu D. Rădulescu is Professor in the Department of Mathematics at the University of Craiova, Romania.