An Elementary Proof of the Harnack Inequality for Non-Negative Infinity-Superharmonic Functions

Date

2001-06-14

Authors

Bhattacharya, Tilak

Journal Title

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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. Electronic Journal of Differential Equations, 2001(44), pp. 1-8.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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