Harnack's inequality for p-harmonic functions via stochastic games
Analysis of PDEs
2012-04-30 v1 Probability
Abstract
We give a proof of Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Harnack's inequality for p-harmonic functions in the case that avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war game.
Keywords
Cite
@article{arxiv.1204.6119,
title = {Harnack's inequality for p-harmonic functions via stochastic games},
author = {Hannes Luiro and Mikko Parviainen and Eero Saksman},
journal= {arXiv preprint arXiv:1204.6119},
year = {2012}
}