Calculus of Variations

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Jürgen Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig) Xianqing Li-Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig)

Calculus of Variations

Jürgen Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig), Xianqing Li-Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig), B. Bollobas , W. Fulton

$229.95

Hardback

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English

Cambridge University Press
29 March 1999

Calculus of variations

Series: Cambridge Studies in Advanced Mathematics

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues such as Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The prerequisites are knowledge of the basic results from calculus of one and several variables. After having studied this book, the reader will be well equipped to read research papers in the calculus of variations.

By: Jürgen Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig), Xianqing Li-Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig)
Series edited by: B. Bollobas, W. Fulton, A. Katok
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 64
Dimensions: Height: 236mm, Width: 157mm, Spine: 23mm
Weight: 590g
ISBN: 9780521642033
ISBN 10: 0521642035
Series: Cambridge Studies in Advanced Mathematics
Pages: 340
Publication Date: 29 March 1999
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Part I. One-Dimensional Variational Problems: 1. The classical theory; 2. Geodesic curves; 3. Saddle point constructions; 4. The theory of Hamilton and Jacobi; 5. Dynamic optimization; Part II. Multiple Integrals in the Calculus of Variations: 6. Lebesgue integration theory; 7. Banach spaces; 8. Lp and Sobolev spaces; 9. The direct methods; 10. Nonconvex functionals: relaxation; 11. G-convergence; 12. BV-functionals and G-convergence: the example of Modica and Mortola; Appendix A. The coarea formula; Appendix B. The distance function from smooth hypersurfaces; 13. Bifurcation theory; 14. The Palais–Smale condition and unstable critical points of variational problems.

Reviews for Calculus of Variations

This modern self-contained exposition...is an excellent textbook for graduate students and a good source of information in the calculus of variations. Mathematical Reviews

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Calculus of Variations

Jürgen Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig), Xianqing Li-Jost (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig), B. Bollobas , W. Fulton

$229.95

Hardback

Reviews for Calculus of Variations

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