This textbook on the calculus of variations covers from the basics to the modern aspects of the theory.
Inhaltsverzeichnis
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.
