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.
Rezensionen / Stimmen
'... 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
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Worked examples or Exercises; 20 Halftones, black and white; 10 Line drawings, black and white
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-0-521-11782-1 (9780521117821)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
Autor*in
Universitatea 'Babes-Bolyai' Cluj-Napoca, Romania
Professor and Senior Researcher
Universitatea 'Babes-Bolyai' 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.
