Bhattacharya, Tilak2020-06-102020-06-102001-06-14Bhattacharya, 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. 1-8.1072-6691https://hdl.handle.net/10877/11601We 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.Text8 pages1 file (.pdf)enAttribution 4.0 InternationalViscosity solutionsHarnack inequalityInfinite harmonic operatorDistance functionArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.