On the Approximation of Anisotropic Energy Functionals by Riemannian Energies via Homogenization

Till Knoke

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arXiv · 1704.04597

On the Approximation of Anisotropic Energy Functionals by Riemannian Energies via Homogenization

Till Knoke

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Abstract

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.

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BibTeX RIS

Till Knoke. 2017-04-15. On the Approximation of Anisotropic Energy Functionals by Riemannian Energies via Homogenization. https://arxiv.org/abs/1704.04597

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