HAL : hal-00179690, version 2

arXiv : 1009.0685

DOI : 10.4171/JEMS/242

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Journal of the European Mathematical Society 13 (2011) 1-26

Versions disponibles :

v1 (16-10-2007)

v2 (03-09-2010)

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

Guy Barles 1, Emmanuel Chasseigne 1, Cyril Imbert 2

(2011)

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.

1 :	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours
2 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : Hölder regularity – integro-differential equations – Lévy operators – general non-local operators – viscosity solutions

hal-00179690, version 2

http://hal.archives-ouvertes.fr/hal-00179690

oai:hal.archives-ouvertes.fr:hal-00179690

Contributeur : Cyril Imbert <>

Soumis le : Vendredi 3 Septembre 2010, 16:09:26

Dernière modification le : Vendredi 4 Mars 2011, 22:00:36