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Article Dans Une Revue Journal of Differential Equations Année : 2011

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

Résumé

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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Dates et versions

hal-00366901 , version 1 (09-03-2009)
hal-00366901 , version 2 (15-05-2009)
hal-00366901 , version 3 (29-07-2010)

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Citer

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