# Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

Abstract : This paper is concerned with Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on $x$ and also a large class of equations, including Bellman-Isaacs Equations.
Keywords :
Type de document :
Article dans une revue
Journal of the European Mathematical Society, European Mathematical Society, 2011, 13, pp.1-26. 〈10.4171/JEMS/242〉

Littérature citée [18 références]

https://hal.archives-ouvertes.fr/hal-00179690
Contributeur : Cyril Imbert <>
Soumis le : vendredi 3 septembre 2010 - 16:09:26
Dernière modification le : mercredi 21 mars 2018 - 10:54:03
Document(s) archivé(s) le : samedi 4 décembre 2010 - 02:53:17

### Fichiers

HNL-hal2.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Guy Barles, Emmanuel Chasseigne, Cyril Imbert. Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations. Journal of the European Mathematical Society, European Mathematical Society, 2011, 13, pp.1-26. 〈10.4171/JEMS/242〉. 〈hal-00179690v2〉

### Métriques

Consultations de la notice

## 427

Téléchargements de fichiers