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

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 Holder continuity of solutions can be directly derived from recent Krylov-Safonov type regularity results in the singula...

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Bibliographic Details
Published inRevista matemática iberoamericana Vol. 40; no. 2; p. 1023
Main Authors Arroyo, Angel, Parviainen, Mikko
Format Journal Article
LanguageSpanish
Published European Mathematical Society Publishing House 01.06.2024
Subjects
Analysis
Differential equations
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Summary: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 Holder 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 Holder estimate, p-Laplacian, Pucci extremal operator, tug-of-war with noise.
ISSN:0213-2230
DOI:10.4171/RMI/1462