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.