Date
2011
Notes
This second version [of the WP version]includes additional results about quadratic non-linearities and a comparison with (and extension of) recent results.
Dewey
Probabilités et mathématiques appliquées
Sujet
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
Journal issue
Journal of Differential Equations
Volume
250
Number
3
Publication date
2011
Article pages
1553-1574
Publisher
Elsevier
Type
Article accepté pour publication ou publié
Abstract (EN)
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.
