Variational Principles in Mathematical Physics, Geometry, and Economics

Qualitative Analysis of Nonlinear Equations and Unilateral Problems

Alexandru Kristály, Vicenţiu D. Rădulescu, Csaba Varga (Autoren)

Buch | Hardcover

386 Seiten

2010
Cambridge University Press (Verlag)
978-0-521-11782-1 (ISBN)

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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.

Alexandru Kristály is Associate Professor in the Department of Economics at the University of Babeş-Bolyai in Cluj-Napoca, Romania. Vicenţiu D. Rădulescu is Professor in the Department of Mathematics at the University of Craiova, Romania. Csaba Gyorgy Varga is Professor in the Department of Mathematics at the University of Babeş-Bolyai in Cluj-Napoca, Romania.

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.

Erscheint lt. Verlag	19.8.2010
Reihe/Serie	Encyclopedia of Mathematics and its Applications
Zusatzinfo	Worked examples or Exercises; 20 Halftones, black and white; 10 Line drawings, black and white
Verlagsort	Cambridge
Sprache	englisch
Maße	163 x 236 mm
Gewicht	720 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-521-11782-8 / 0521117828
ISBN-13	978-0-521-11782-1 / 9780521117821
Zustand	Neuware