Differential and Integral Equations

On the existence and uniqueness of $p$-harmonious functions

Hannes Luiro, Mikko Parviainen, and Eero Saksman

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We give a self-contained and short proof for the existence, uniqueness and measurability of the $p$-harmonious functions in the case $2\le p < \infty$. The proofs only use elementary analytic tools. As a consequence, we obtain existence, uniqueness and measurability of value functions for the tug-of-war game with noise.

Article information

Differential Integral Equations, Volume 27, Number 3/4 (2014), 201-216.

First available in Project Euclid: 30 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A35: Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx} 35J92: Quasilinear elliptic equations with p-Laplacian 91A05: 2-person games 91A15: Stochastic games


Luiro, Hannes; Parviainen, Mikko; Saksman, Eero. On the existence and uniqueness of $p$-harmonious functions. Differential Integral Equations 27 (2014), no. 3/4, 201--216. https://projecteuclid.org/euclid.die/1391091363

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