Direct Methods in the Calculus of Variations

I. Convex analysis and the scalar case

1. Introduction

2. Convex sets and convex functions

3. Lower semicontinuity and existence theorems

4. The one dimensional case

II. Quasiconvex analysis and the vectorial case

5. Polyconvex, quasiconvex and rank one convex functions

6. Polyconvex, quasiconvex and rank one convex envelopes

7. Polyconvex, quasiconvex and rank one convex sets

8. Lower semi continuity and existence theorems in the vectorial case

III. Relaxation and non-convex problems

9. Relaxation theorems

10. Implicit partial differential equations

11. Existence of minima for non-quasiconvex integrands

IV. Miscellaneous

12. Function spaces

13. Singular values

14. Some underdetermined partial differential equations

15. Extension of Lipschitz functions on Banach spaces

DRM-restrictions

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Avainsanat: MATHEMATICS / General MAT000000