1. Minimum problems. Compactness and lower semicontinuity
2. Minimum problems for integral functionals in Lebesgue spaces. Weak
3. Relaxation for integral functionals in Lebesgue spaces. Convex
and lsc envelopes. Young-measure solutions.
4. Relaxation on spaces of measures. The blow-up method.
5. Non convex problems on spaces of measures. Subadditivity.
6. Problems in Sobolev spaces. Quasiconvexity and polyconvexity.
7. Problems in spaces of functions with bounded variation and for sets
8. Gamma-convergence. Homogenization. Limits of Riemannian metrics.
9. Approximate solutions. Finite-difference
approximations. Vanishing-viscosity approximation.
A. Braides and A. Defranceschi. Homogenization of Multiple Integrals.
Oxford UP, 1998. (Part
A. Braides. Gamma-convergence for Beginners. Oxford UP, 2002.
B. Dacorogna. Direct Methods in the Calculus of Variations (Second
Edition). Springer, 2008.
I. Fonseca and G.Leoni. Modern Methods in the Calculus of Variations:
L^p Spaces. Springer, 2007.