Variational Principles in Mathematical Physics, Geometry, and Economics
Qualitative Analysis of Nonlinear Equations and Unilateral Problems
Published on 19. August 2010
Book
Hardback
386 pages
978-0-521-11782-1 (ISBN)
Description
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.
Reviews / Votes
'... 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 MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 20 Halftones, black and white; 10 Line drawings, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 25 mm
Weight
743 gr
ISBN-13
978-0-521-11782-1 (9780521117821)
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Schweitzer Classification
Other editions
Additional editions
Alexandru Kristaly | Vicentiu D. Radulescu | Csaba Varga
Variational Principles in Mathematical Physics, Geometry, and Economics
Qualitative Analysis of Nonlinear Equations and Unilateral Problems
E-Book
10/2014
1st Edition
Cambridge University Press
€97.49
Available for download
Persons
Alexandru Kristaly is Associate Professor in the Department of Economics at the University of Babes-Bolyai in Cluj-Napoca, Romania. Vicentiu D. Radulescu 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 Babes-Bolyai in Cluj-Napoca, Romania.
Content
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.