Variational principles in mathematical physics, geometry, and economics: qualitative analysis of nonlinear equations and unilateral problems
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 f...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 136 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xv, 368 pages) |
| ISBN: | 9780511760631 |
| DOI: | 10.1017/CBO9780511760631 |
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| 505 | 8 | |a 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 | |
| 520 | |a 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 | ||
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| contents | 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 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| id | DE-604.BV043942083 |
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| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511760631 |
| language | English |
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| spelling | Kristály, Alexandru Verfasser aut Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba Gyorgy Varga Variational Principles in Mathematical Physics, Geometry, & Economics Cambridge Cambridge University Press 2010 1 online resource (xv, 368 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 136 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Calculus of variations Anwendung (DE-588)4196864-5 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 s Anwendung (DE-588)4196864-5 s 1\p DE-604 Rădulescu, Vicenţiu D. 1958- Sonstige oth Varga, Csaba Gyorgy Sonstige oth Erscheint auch als Druckausgabe 978-0-521-11782-1 https://doi.org/10.1017/CBO9780511760631 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kristály, Alexandru Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems 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 Calculus of variations Anwendung (DE-588)4196864-5 gnd Variationsprinzip (DE-588)4062354-3 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4062354-3 |
| title | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_alt | Variational Principles in Mathematical Physics, Geometry, & Economics |
| title_auth | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_exact_search | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_full | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba Gyorgy Varga |
| title_fullStr | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba Gyorgy Varga |
| title_full_unstemmed | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba Gyorgy Varga |
| title_short | Variational principles in mathematical physics, geometry, and economics |
| title_sort | variational principles in mathematical physics geometry and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_sub | qualitative analysis of nonlinear equations and unilateral problems |
| topic | Calculus of variations Anwendung (DE-588)4196864-5 gnd Variationsprinzip (DE-588)4062354-3 gnd |
| topic_facet | Calculus of variations Anwendung Variationsprinzip |
| url | https://doi.org/10.1017/CBO9780511760631 |
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