Singular perturbations for an elliptic operator in the Heisenberg group - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Singular perturbations for an elliptic operator in the Heisenberg group

Résumé

We study some classes of singular perturbation problems where the dynamics of the fast variables evolve in the whole space obeying to an infinitesimal operator which is subelliptic and ergodic. We prove that the corresponding ergodic problem admits a solution which is globally Lipschitz continuous and it has at most a logarithmic growth at infinity. The main result of this paper establishes that as $\epsilon \to 0$, the value functions of the singular perturbation problems converge locally uniformly to the solution of an effective problem whose operator and data are explicitly given in terms of the invariant measure for the ergodic operator.
Fichier principal
Vignette du fichier
Pert.Sing-01-02-17.pdf (239.54 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01455449 , version 1 (03-02-2017)
hal-01455449 , version 2 (03-03-2017)

Identifiants

  • HAL Id : hal-01455449 , version 1

Citer

Paola Mannucci, Claudio Marchi, Nicoletta Tchou. Singular perturbations for an elliptic operator in the Heisenberg group. 2017. ⟨hal-01455449v1⟩
472 Consultations
210 Téléchargements

Partager

Gmail Facebook X LinkedIn More