Electron. J. Diff. Eqns., Vol. 2006(2006), No. 122, pp. 14.
A remark on
infinityharmonic functions
Yifeng Yu
Abstract:
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 [2] in two dimensions. When the solution
is
,
Evans [6] established a Harnack inequality
for
,
which implies that nonconstant
solutions
have no interior critical points for any dimension.
Our method is strongly motivated by the work in [6].
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
email: yifengyu@math.utexas.edu 
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