Results dealing with the behavior of the integrated density of states of random divergence operators

Hatem Najar

doi:10.1016/j.crma.2007.02.001

Partial Differential Equations

Results dealing with the behavior of the integrated density of states of random divergence operators
[Des résultats sur le comportement de la densité d'états integrèe de l'opérateur de divergence aléatoire]

Présenté par : Gilles Lebeau

Hatem Najar ¹

¹ I.P.E.I. Monastir, rue Ibn Eljazzar, 5019 Monastir, Tunisia

Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 367-372.

Résumé
Abstract

Dans cette Note on généralise et en améliore des résultats prouvés pour les opérateurs acoustique par Najar (2003). Il concerne le comportement de la densité d'états intégrée de l'opérateur de divergence aléatoire ayant la forme $H_{ω} = \sum_{i, j = 1}^{d} \partial_{x_{i}} a_{i, j} (ω, x) \partial_{x_{j}}$ aux bords internes du spectre.

In this Note we generalize and improve results proven for acoustic operators given by Najar in 2003. It deals with the behavior of the integrated density of states of random divergence operators of the form $H_{ω} = \sum_{i, j = 1}^{d} \partial_{x_{i}} a_{i, j} (ω, x) \partial_{x_{j}}$ on the internal band edges of the spectrum.

Reçu le : 2006-08-31
Accepté le : 2007-01-25
Publié le : 2007-03-12

DOI : 10.1016/j.crma.2007.02.001

Affiliations des auteurs :

Hatem Najar ¹

¹ I.P.E.I. Monastir, rue Ibn Eljazzar, 5019 Monastir, Tunisia

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Hatem Najar. Results dealing with the behavior of the integrated density of states of random divergence operators. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 367-372. doi : 10.1016/j.crma.2007.02.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.02.001/

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