Geodesic
A remark on $C^2$ infinity-harmonic functions
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we prove that any nonconstant, $C^2$ solution of the infinity Laplacian equation $u_{x_i}u_{x_j}u_{x_ix_j}=0$ can not have interior critical points. This result was first proved by Aronsson [2] in two dimensions. When the solution is $C^4$, Evans [6] established a Harnack inequality for $|Du|$, which implies that non-constant $C^4$ solutions have no interior critical points for any dimension. Our method is strongly motivated by the work in [6].
Classification : 35B38
Keywords: infinity Laplacian equation, infinity harmonic function, viscosity solutions 
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     author = {Yu, Yifeng},
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Yu, Yifeng. A remark on $C^2$ infinity-harmonic functions. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a46/