Plane-like minimizers and differentiability of the stable norm
Analysis of PDEs
2012-10-16 v2 Differential Geometry
Dynamical Systems
Abstract
In this paper we investigate the strict convexity and the differentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always differentiable in totally irrational directions, while in other directions, it is differentiable if and only if the corresponding plane-like minimizers satisfying a strong Birkhoff property foliate the torus. We also discuss the issue of the uniqueness of the correctors for the corresponding homogenization problem.
Keywords
Cite
@article{arxiv.1205.1289,
title = {Plane-like minimizers and differentiability of the stable norm},
author = {Antonin Chambolle and Michael Goldman and Matteo Novaga},
journal= {arXiv preprint arXiv:1205.1289},
year = {2012}
}
Comments
Accepted in J. Geometric Analysis