An easy proof of Jensen’s theorem on the uniqueness of infinity harmonic functions

By S. Armstrong, Charles K. Smart. 2009

136 citations recorded by the source corpus.

We present a new, easy, and elementary proof of Jensen’s Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/cc8a8cb84dab879db29f0246bcee4a2c3dac4af9

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In Applied Mathematics

Citations in the corpus

On the definition and properties of p-harmonious functions (2012, background): “Armstrong-Smart [1], [2] (note that this last reference does not use tools from probability theory).”
A finite difference approach to the infinity Laplace equation and tug-of-war games (2009, methodology): “Given a strategy I for Player I and a strategy II for Player II, we denote by FI( I, II) and FII( I, II) the expected value of the expression (2.7) if the game terminates with probability one, and this expectation is defined in [ 1 ,1].”
Harnack's Inequality for p-Harmonic Functions via Stochastic Games (2012, background): “This has inspired further studies to many different directions, see for example [2, 21], as well as led to simplified proofs in the theory of PDEs, see for example [1].”