  In their paper, Braides, Buttazzo and Fragala proved the density of
Riemannian energies in the class of Finsler energy functionals with respect to
$\Gamma$-convergence in the one-dimensional case. In this thesis we prove that
one of the main tools in that paper, a homogenization theorem, can be extended
to arbitrary dimension, however, the density result cannot be generalized to
higher dimensions. In fact, we construct counterexamples that show: there are
anisotropic energy functionals, such as Finsler energies, Cartan functionals
and their dominance functionals that cannot be $\Gamma$-approximated by
Riemannian energies.
