An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift

François Hamel; Nikolai Nadirashvili; Emmanuel Russ

doi:10.1016/j.crma.2005.01.012

Partial Differential Equations

An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift

Presented by: Haïm Brezis

François Hamel ¹; Nikolai Nadirashvili ²; Emmanuel Russ ¹

¹ Université Aix-Marseille III, LATP, avenue Escadrille Normandie-Niemen, 13397 Marseille cedex 20, France
² CNRS, LATP, CMI, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 347-352.

Abstract
Résumé

We generalize the classical Rayleigh–Faber–Krahn inequality to the case of the Dirichlet Laplacian with a drift. We also solve some optimization problems for the principal eigenvalue of the operator $- Δ + v \cdot \nabla$ in a fixed domain with a control of the drift v in $L^{\infty}$ .

Nous généralisons l'inégalité classique de Rayleigh–Faber–Krahn au cas du laplacien Dirichlet avec un terme de transport. Nous résolvons également des problèmes d'optimisation pour la valeur propre principale de l'opérateur $- Δ + v \cdot \nabla$ dans un domaine fixé et avec un contrôle $L^{\infty}$ sur le terme de transport v.

Received: 2004-12-16
Published online: 2005-02-09

DOI: 10.1016/j.crma.2005.01.012

Author's affiliations:

François Hamel ¹; Nikolai Nadirashvili ²; Emmanuel Russ ¹

¹ Université Aix-Marseille III, 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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     title = {An isoperimetric inequality for the principal eigenvalue of the {Laplacian} with drift},
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François Hamel; Nikolai Nadirashvili; Emmanuel Russ. An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift. Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 347-352. doi : 10.1016/j.crma.2005.01.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.012/

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