Minoration de la résolvante dans le cas captif

Jean-François Bony; Nicolas Burq; Thierry Ramond

doi:10.1016/j.crma.2010.10.025

Équations aux dérivées partielles/Physique mathématique

Minoration de la résolvante dans le cas captif

Présenté par : Jean-Michel Bony

Jean-François Bony ¹ ; Nicolas Burq ² ; Thierry Ramond ²

¹ IMB (UMR CNRS 5251), université Bordeaux 1, 33405 Talence, France
² LMO (UMR CNRS 8628), université Paris Sud 11, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1279-1282.

Résumé
Abstract

Dans cette note, on démontre une minoration universelle optimale sur la norme de la résolvante tronquée pour les opérateurs de Schrödinger semiclassiques près d'une énergie captive. En particulier, ce résultat implique que des majorations connues pour des captures hyperboliques sont optimales. La preuve repose sur un argument de X.P. Wang et la propagation en temps d'Ehrenfest des états cohérents.

In this note, we prove an optimal universal lower bound on the truncated resolvent for semiclassical Schrödinger operators near a trapping energy. In particular, this shows that known upper bounds for hyperbolic trapping are optimal. The proof rely on an idea of X.P. Wang, and on propagation of coherent states for Ehrenfest times.

Reçu le : 2010-09-29
Accepté le : 2010-10-18
Publié le : 2010-11-10

DOI : 10.1016/j.crma.2010.10.025

Affiliations des auteurs :

Jean-François Bony ¹ ; Nicolas Burq ² ; Thierry Ramond ²

¹ IMB (UMR CNRS 5251), université Bordeaux 1, 33405 Talence, France
² LMO (UMR CNRS 8628), université Paris Sud 11, 91405 Orsay cedex, France

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Jean-François Bony; Nicolas Burq; Thierry Ramond. Minoration de la résolvante dans le cas captif. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1279-1282. doi : 10.1016/j.crma.2010.10.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.025/

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