Estimates for Smooth Absolutely Minimizing Lipschitz Extensions
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I present some elementary maximum principle arguments, estab- lishing interior gradient bounds and Harnack inequalities for both u and |Du|, where u is a smooth solution of the degenerate elliptic PDE ∆∞u = 0. These calculations in particular extend to higher dimensions G. Aronsson’s assertion  that a nonconstant, smooth solution can have no interior critical point.
CitationEvans, L. C. (1993). Estimates for smooth absolutely minimizing Lipschitz extensions. Electronic Journal of Differential Equations, 1993(03), pp. 1-9.
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