1.CMAP école Polytechnique,CNRS,Palaiseau,France;2.Max Planck Institute for Mathematics in the Sciences,Leipzig,Germany;3.Dipartimento di Matematica,Università di Padova,Padova,Italy
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.