An Elementary Proof of the Harnack Inequality for Non-Negative Infinity-Superharmonic Functions
Southwest Texas State University, Department of Mathematics
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.
Viscosity solutions, Harnack inequality, Infinite harmonic operator, Distance function
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.
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