An Elementary Proof of the Harnack Inequality for Non-Negative Infinity-Superharmonic Functions
Date
2001-06-14
Authors
Bhattacharya, Tilak
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We present an elementary proof of the Harnack inequality for non-negative viscosity supersolutions of Δ∞u = 0. This was originally proven by Lindqvist and Manfredi using sequences of solutions of the p-Laplacian. We work directly with the Δ∞ operator using the distance function as a test function. We also provide simple proofs of the Liouville property, Hopf boundary point lemma and Lipschitz continuity.
Description
Keywords
Viscosity solutions, Harnack inequality, Infinite harmonic operator, Distance function
Citation
Bhattacharya, T. (2001). An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. <i>Electronic Journal of Differential Equations, 2001</i>(44), pp. 1-8.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.