Year: 2022
Author: Fang Liu, Fei Meng, Xiaoyan Chen
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 439–450
Abstract
In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2020-0002
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 439–450
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: $β$−biased infinity Laplacian viscosity solution exponential cone Harnack inequality Lipschitz regularity.