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