Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 148, pp. 1-11.

Title: Remarks on the gradient of an infinity-harmonic function

Author: Tilak Bhattacharya (Western Kentucky Univ., Bowling Green, KY, USA)

Abstract: 
 In this work we (i) prove a maximum principle for the
 modulus of the gradient of infinity-harmonic functions,
 (ii) prove some local properties of the modulus, and
 (iii) prove that if the modulus is constant on the boundary
 of a planar disc then it is constant inside.
 
Submitted August 10, 2007. Published November 05, 2007.
Math Subject Classifications: 35J60, 35J70.
Key Words: Infinity-harmonic; gradient; maximum principle.