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Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

Imbert, Cyril (2011), Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations, Journal of Differential Equations, 250, 3, p. 1553-1574. http://dx.doi.org/10.1016/j.jde.2010.07.005

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00366901/en/
Date
2011
Journal name
Journal of Differential Equations
Volume
250
Number
3
Publisher
Elsevier
Pages
1553-1574
Publication identifier
Metadata
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Author(s)
Imbert, Cyril cc
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.
Subjects / Keywords
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