Minimization of $\lambda_2(\Omega)$ with a perimeter constraint

Abstract : We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two points where the curvature vanishes. In $N$ dimensions, we prove a more general existence theorem for a class of functionals which is decreasing with respect to set inclusion and $\gamma$ lower semicontinuous.
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Article dans une revue
Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2009, 58 (6), pp.2709-2728
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https://hal.archives-ouvertes.fr/hal-00201946
Contributeur : Antoine Henrot <>
Soumis le : mardi 2 juin 2009 - 15:31:48
Dernière modification le : mercredi 15 mars 2017 - 12:13:17
Document(s) archivé(s) le : samedi 26 novembre 2016 - 09:54:09

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  • HAL Id : hal-00201946, version 3
  • ARXIV : 0904.2193

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Dorin Bucur, Giuseppe Buttazzo, Antoine Henrot. Minimization of $\lambda_2(\Omega)$ with a perimeter constraint. Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2009, 58 (6), pp.2709-2728. <hal-00201946v3>

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