Electron. J. Diff. Eqns., Vol. 1995(1995), No. 04, pp. 1-5.

The Harnack Inequality for $\infty$-harmonic Functions

Peter Lindqvist & Juan J. Manfredi

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.

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Peter Lindqvist
Department of Mathematics, Norwegian Institute of Technology, N-7034 Trondheim, Norway
e-mail: lqvist@imf.unit.no

Juan J. Manfredi
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
e-mail: juanjo@na0b.math.pitt.edu

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