Hölder estimate for a tug-of-war game with 1 < p < 2 from Krylov–Safonov regularity theory

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 Hölder 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.