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arXiv · 2212.10807

H\"older estimate for a tug-of-war game with $1<p<2$ from Krylov-Safonov regularity theory

Ángel Arroyo·Mikko Parviainen
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Abstract

We propose a new version of the tug-of-war game and a corresponding dynamic programming principle related to the $p$-Laplacian with $1<p<2$. For this version, the asymptotic H\"older continuity of solutions can be directly derived from recent Krylov-Safonov type regularity results in the singular case. Moreover, existence of a measurable solution can be obtained without using boundary corrections. We also establish a comparison principle.

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Ángel Arroyo, Mikko Parviainen. 2022-12-21. H\"older estimate for a tug-of-war game with $1<p<2$ from Krylov-Safonov regularity theory. https://arxiv.org/abs/2212.10807

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