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| HAL : hal-00115319, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Archive for Rational Mechanics and Analysis 169 (2003) 73-87 |
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| Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions |
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| Antoine Henrot 1, 2Edouard Oudet 3 |
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| (2003) |
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| In this paper, we are interested in the minimization of the second eigenvalue of the Laplacian with Dirichlet boundary conditions amongst convex plane domains with given area. The natural candidate to be the optimum was the ''stadium'', convex hull of two identical tangent disks. We refute this conjecture. Nevertheless, we prove existence of a minimzer. We also study some qualitative properties of the minimizer (regularity, geometric properties). |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| 2 : | CORIDA (INRIA Lorraine / IECN / MMAS) |
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INRIA – CNRS : UMR7122 – CNRS : UMR7502 – Université Paul Verlaine - Metz – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| 3 : | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| Equations aux derivees partielles |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00115319, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00115319 | |
| oai:hal.archives-ouvertes.fr:hal-00115319 | |
| Contributeur : Antoine Henrot | |
| Soumis le : Mardi 21 Novembre 2006, 10:06:16 | |
| Dernière modification le : Mercredi 27 Avril 2011, 11:40:17 | |
