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Variational Principles in Mathematical Physics, Geometry, and Economics
Qualitative Analysis of Nonlinear Equations and Unilateral Problems


Part of Encyclopedia of Mathematics and its Applications

Jean Mawhin
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  • Date Published: August 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521117821

£ 116.00

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About the Authors
  • 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.

    • 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    • Contains new, previously unpublished material
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: August 2010
    • format: Hardback
    • isbn: 9780521117821
    • length: 386 pages
    • dimensions: 236 x 163 x 28 mm
    • weight: 0.72kg
    • contains: 30 b/w illus. 45 exercises
    • availability: Available
  • Table of Contents

    Foreword Jean Mawhin
    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

  • Authors

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

    Vicenţiu D. Rădulescu, Institutul de Matematica 'Simion Stoilow' al Academiei Romane Bucuresti, Romania
    Vicenţiu D. Rădulescu is Professor in the Department of Mathematics at the University of Craiova, Romania.

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


    Jean Mawhin

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