English

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 p>2p>2 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}
}