Electron. J. Diff. Eqns., Vol. 2007(2007), No. 148, pp. 1-11.

Remarks on the gradient of an infinity-harmonic function

Tilak Bhattacharya

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 5, 2007.
Math Subject Classifications: 35J60, 35J70.
Key Words: Infinity-harmonic; gradient; maximum principle.

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Tilak Bhattacharya
Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101, USA
email: tilak.bhattacharya@wku.edu

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