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| HAL : hal-00511096, version 1 |
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| Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character 467, 2130 (2011) 1577-1603 |
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| On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian |
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| Pedro R.S. Antunes 1Antoine Henrot 2, 3 |
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| (06/2011) |
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| In this paper we study the set of points, in the plane, defined by $\{(x,y)=(\lambda_1(\Omega),\lambda_2(\Omega)),\ |\Omega|=1\},$ where $(\lambda_1(\Omega),\lambda_2(\Omega))$ are either the two first eigenvalues of the Dirichlet-Laplacian, or the two first non trivial eigenvalues of the Neumann-Laplacian. We consider the case of general open sets together with the case of convex open domains. We give some qualitative properties of these sets, show some pictures obtained through numerical computations and state several open problems. |
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| 1 : | Grupo de Física Matemática - Group of Mathematical Physics (GFM) |
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Universidade de Lisboa |
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| 2 : | 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 (INPL) |
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| 3 : | CORIDA (INRIA Nancy - Grand Est / IECN / LMAM) |
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INRIA – CNRS : UMR7502 – Université de Lorraine |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Théorie spectrale |
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| Dirichlet Laplacian – Neumann Laplacian – Eigenvalues – Shape optimization |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00511096, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00511096 | |
| oai:hal.archives-ouvertes.fr:hal-00511096 | |
| Contributeur : Antoine Henrot | |
| Soumis le : Lundi 23 Août 2010, 17:32:30 | |
| Dernière modification le : Lundi 2 Mai 2011, 10:31:47 | |
