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

Abstract : 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.
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Cited literature [27 references]

https://hal.archives-ouvertes.fr/hal-00366901
Contributor : Cyril Imbert <>
Submitted on : Thursday, July 29, 2010 - 12:10:55 PM
Last modification on : Wednesday, February 19, 2020 - 8:59:50 AM
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### Citation

Cyril Imbert. Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations. Journal of Differential Equations, Elsevier, 2011, 250 (3), pp.1553--1574. ⟨10.1016/j.jde.2010.07.005⟩. ⟨hal-00366901v3⟩

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