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| HAL: hal-00694872, version 1 |
| arXiv: 1205.1289 |
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| Available versions: | v1 (2012-05-07) | v2 (2012-10-15) |
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| Plane-like minimizers and differentiability of the stable norm |
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| Antonin Chambolle 1Michael Goldman 1 |
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| (2012-05-07) |
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| 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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| 1: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 2: | Dipartimento di Matematica Pura ed Applicata |
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Università degli studi di Padova |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Differential Geometry Mathematics/Dynamical Systems |
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| Plane-like minimizers – Geometric KAM Theory – Minimal surfaces – Birkhoff property – calibrations |
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| hal-00694872, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00694872 | |
| oai:hal.archives-ouvertes.fr:hal-00694872 | |
| From: Michael Goldman | |
| Submitted on: Monday, 7 May 2012 01:17:44 | |
| Updated on: Monday, 7 May 2012 08:27:19 | |
