@Article{ATA-38-4,
author = {Liu, Fang and Meng, Fei and Xiaoyan, Chen},
title = {Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation},
journal = {Analysis in Theory and Applications},
year = {2022},
volume = {38},
number = {4},
pages = {439--450},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2020-0002},
url = {https://global-sci.com/article/73765/regularity-of-viscosity-solutions-of-the-biased-infinity-laplacian-equation}
}