On the approximation of anisotropic energy functionals by Riemannian energies via homogenization

  • Über die Approximation von anisotropen Energiefunktionalen durch Riemannsche Energien mittels Homogenisierung

Knoke, Till; von der Mosel, Heiko (Thesis advisor); Wagner, Alfred (Thesis advisor)

Aachen (2016)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen, 2016

Abstract

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.

Institutions

  • Mathematics Teaching and Research Area [112120]
  • Department of Mathematics [110000]