Electronic Journal of Differential Equations,
Vol. 1995(1995), No. 04, pp. 1-5.

Title: The Harnack Inequality for $\infty$-harmonic Functions 

Authors: Peter Lindqvist (Norwegian Institute of Technology)
         Juan J. Manfredi (Univ. of Pittsburgh, PA, USA)

Abstract: The Harnack inequality for nonnegative viscosity 
solutions of the equation  
          $ \Delta_\infty u = 0 $ 
is proved, extending a previous result of L.C. Evans for smooth
solutions.  The method of proof consists in considering  
          $ \Delta_\infty u = 0 $ 
as the limit as $p\to\infty$ of the more familiar $p$-harmonic
equation $\Delta_p u=0$.

Submitted February 22, 1995. Published April 3, 1995.
Math Subject Classification: 35J70, 26A16.
Key Words: Harnack inequality; $p$-harmonic equations.