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Article Dans Une Revue Journal of Geometric Analysis Année : 2014

Plane-like minimizers and differentiability of the stable norm

Résumé

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.
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Dates et versions

hal-00694872 , version 1 (07-05-2012)
hal-00694872 , version 2 (12-10-2012)

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Antonin Chambolle, Michael Goldman, Matteo Novaga. Plane-like minimizers and differentiability of the stable norm. Journal of Geometric Analysis, 2014. ⟨hal-00694872v2⟩
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