A remark on C2 infinity-harmonic functions
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In this paper, we prove that any nonconstant, C2 solution of the infinity Laplacian equation uₓiuₓj uₓiₓj = 0 can not have interior critical points. This result was first proved by Aronsson  in two dimensions. When the solution is C4, Evans  established a Harnack inequality for |Du|, which implies that non-constant C4 solutions have no interior critical points for any dimension. Our method is strongly motivated by the work in .
CitationYu, Y. (2006). A remark on C2 infinity-harmonic functions. Electronic Journal of Differential Equations, 2006(122), pp. 1-4.
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