Yu, Yifeng2021-07-202021-07-202006-10-06Yu, Y. (2006). A remark on C2 infinity-harmonic functions. <i>Electronic Journal of Differential Equations, 2006</i>(122), pp. 1-4.1072-6691https://hdl.handle.net/10877/13995In 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 [2] in two dimensions. When the solution is C4, Evans [6] 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 [6].Text4 pages1 file (.pdf)enAttribution 4.0 InternationalInfinity Laplacian equationInfinity harmonic functionViscosity solutionsArticle