Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited

Abstract : The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen-Ishii's Lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The proof of this result, which is of course a key ingredient to prove comparison principles, relies on a new definition of viscosity solution for integro-differential equation (equivalent to the two classical ones) which combines the approach with test-functions and sub-superjets.
Type de document :
Article dans une revue
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2008, 25 (3), pp.567-585. 〈10.1016/j.anihpc.2007.02.007〉
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00130169
Contributeur : Guy Barles <>
Soumis le : mardi 30 septembre 2008 - 16:11:52
Dernière modification le : mercredi 21 mars 2018 - 10:54:03
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 16:53:47

Fichiers

IDR_v3.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Guy Barles, Cyril Imbert. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2008, 25 (3), pp.567-585. 〈10.1016/j.anihpc.2007.02.007〉. 〈hal-00130169v3〉

Partager

Métriques

Consultations de la notice

217

Téléchargements de fichiers

447