In this paper, we prove that any nonconstant, solution of the infinity Laplacian equation can not have interior critical points. This result was first proved by Aronsson  in two dimensions. When the solution is , Evans  established a Harnack inequality for , which implies that non-constant solutions have no interior critical points for any dimension. Our method is strongly motivated by the work in .
Submitted June 15, 2006. Published October 6, 2006.
Math Subject Classifications: 35B38.
Key Words: Infinity Laplacian equation; infinity harmonic function; viscosity solutions.
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| Yifeng Yu |
Department of Mathematics
University of Texas
Austin, TX 78712, USA
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