Partial Differential Equations
Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form
Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 169-174.

We prove various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in C2 bounded nonempty domains of Rn. In particular, we obtain a ‘Faber–Krahn’ type inequality for these operators. The proofs use a new rearrangement technique.

On montre divers résultats d'optimisation pour la première valeur propre d'opérateurs elliptiques généraux du second ordre sous forme divergence avec condition au bord de Dirichlet dans des domaines bornés non vides de classe C2 de Rn. En particulier, on obtient une inégalité de type « Faber–Krahn » pour ces opérateurs. Les preuves utilisent une nouvelle méthode de réarrangement.

Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.025
Hamel, François 1; Nadirashvili, Nikolai 2; Russ, Emmanuel 1

1 Université Paul-Cézanne LATP, avenue Escadrille Normandie-Niemen, 13397 Marseille cedex 20, France
2 CNRS, LATP, CMI, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France
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Hamel, François; Nadirashvili, Nikolai; Russ, Emmanuel. Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 169-174. doi : 10.1016/j.crma.2006.11.025. http://www.numdam.org/articles/10.1016/j.crma.2006.11.025/

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