The Harnack Inequality for ∞-Harmonic Functions
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The Harnack inequality for nonnegative viscosity solutions of the equa- tion ∆∞u = 0 is proved, extending a previous result of L.C. Evans for smooth solutions. The method of proof consists in considering ∆∞u = 0 as the limit as p → ∞ of the more familiar p-harmonic equation ∆pu = 0.