Date
2011
Description
This second version [of the WP version]includes additional results about quadratic non-linearities and a comparison with (and extension of) recent results.
Lien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00366901/en/
Indexation documentaire
Probabilités et mathématiques appliquées
Subject
viscosity solutions; singular elliptic equation; Alexandrov-Bakelman-Pucci estimate; non-divergence form; Degenerate fully nonlinear elliptic equation; weak Harnack inequality; local maximum principle; Harnack inequality; Hölder regularity
Nom de la revue
Journal of Differential Equations
Volume
250
Numéro
3
Date de publication
2011
Pages article
1553-1574
Nom de l'éditeur
Elsevier
Type
Article accepté pour publication ou publié
Résumé en anglais
In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when ``the gradient is small''. Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate elliptic equations.
