Calculus of Variations

課程內容

1. Geodesics in the plane are straight lines

2. Banach and Hilbert spaces [GT, Ch.5]

3. Introduction to Schauder estimates, weak derivatives and Sobolev embeddings [GT, Ch.6, 7]

4.  Convergence [E, Ch.1]

5.  Convexity and variation [E, Ch.2, 3; S, 1.1]

6.  Convexity and variation [E, Ch.2, 3; S, 1.1]

7.  Convexity and variation [E, Ch.2, 3; S, 1.1]

8. Constrainted Compactness [E, Ch.4; S, 1.2]

9. Ekeland's principle [S, 1.5]

10. variation with parameters [S, 1.7]

11. Min-Max theory [S, 2.1-2.6]

參考書籍

L. C. Evans, Weak convergence methods for nonlinear partial differential equations, 1990 AMS.

M. Struwe, Variational methods, 1996 Springer.

Gilbarg and Trudinger