*SOME COMMENTS ON VECTORIAL PROBLEMS
Andrea Braides · Oxford University Press eBooks · 2002
This chapter shows that some notions used in a one-dimensional setting can be extended to higher dimensions and vector problems if properly modified. In particular, convexity requirements for lower semicontinuity lead to the notions of quasiconvexity and polyconvexity, and homogenization formulas are proven to hold in a vector setting once the cell-problem formula is discarded, being valid only in a convex setting. New phenomena arise that are not meaningful in one dimension, as the instability of polyconvexity by homogenization and the density of isotropic quadratic functionals in all quadratic forms.