Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

Guy Barles 1, 2 Olivier Ley 3, * Erwin Topp 4
* Auteur correspondant
1 FRDP - Fédération de recherche Denis Poisson
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Departamento de Matematica y C.C.
Abstract : In this paper, we provide suitable adaptations of the " weak version of Bernstein method " introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed " uniformly el-liptic " (maybe in the nonlocal sense) but which do not satisfy the usual " growth condition " on the gradient term allowing to use (for example) the Ishii-Lions' method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.
Keywords : Lipschitz regularity nonlinear PDEs {Integro-differential equations strong maximum principle comparison principle large time behavior
Type de document :
Article dans une revue
Nonlinearity, IOP Publishing, 2017, 30 (2), pp.703-734. 〈10.1088/1361-6544/aa527f〉
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger
https://hal.archives-ouvertes.fr/hal-01278603
Contributeur : Olivier Ley <>
Soumis le : mercredi 24 février 2016 - 15:32:59
Dernière modification le : samedi 24 mars 2018 - 01:54:57
Document(s) archivé(s) le : mercredi 25 mai 2016 - 10:37:41

Fichiers

lipschitz_Bernstein.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

IRMAR | UNIV-ORLEANS | INSMI | LMPT | IRMAR-AN | CHL | TDS-MACS | UNAM | INRIA | IRMAR-INSA | INRIA2017 | UNIV-RENNES2 | UR2-HB | IDP | UNIV-RENNES

Citation

Guy Barles, Olivier Ley, Erwin Topp. Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. Nonlinearity, IOP Publishing, 2017, 30 (2), pp.703-734. 〈10.1088/1361-6544/aa527f〉. 〈hal-01278603〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

435

Téléchargements de fichiers

170