On the approximation of anisotropic energy functionals by Riemannian energies via homogenization
Knoke, Till; von der Mosel, Heiko (Thesis advisor); Wagner, Alfred (Thesis advisor)
Aachen (2016) [Dissertation / PhD Thesis]
Page(s): 1 Online-Ressource (ix, 62 Seiten) ; Diagramme
In "Riemannian Approximation of Finsler metrics", 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 "Riemannian Approximation of Finsler metrics", 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.