Arroyo, Ángel, Parviainen, Mikko
Hölder estimate for a tug-of-war game with 1 < p < 2 from Krylov–Safonov regularity theory
Revista Matemática Iberoamericana. 2024, 40(3): 1023-1044. https://doi.org/10.4171/rmi/1462
URI: http://hdl.handle.net/10045/140159
DOI: 10.4171/rmi/1462
ISSN: 0213-2230 (Print)
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.
Keywords:ABP-estimate, Elliptic non-divergence form partial differential equation with bounded and measurable coefficients, Dynamic programming principle, Local Hölder estimate, p-Laplacian, Pucci extremal operator, Tug-of-war with noise
EMS Press
info:eu-repo/semantics/article