Peres, Y., Pete, G. and Somersille, S. (2010) Biased Tug-of-War, the Biased Infinity Laplacian, and Comparison with Exponential Cones. Calculus of Variations and Partial Differential Equations, 38, 541-564.
https://doi.org/10.1007/s00526-009-0298-2

has been cited by the following article:

• TITLE: Lipschitz Regularity of Viscosity Solutions to the Infinity Laplace Equation

  AUTHORS: Xiao Han, Fang Liu

  KEYWORDS: Normalized Infinity Laplacian, Viscosity Solution, Lipschitz Regularity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 25, 2023

  ABSTRACT: In this paper, we study the viscosity solutions of the Neumann problem in a bounded C2 domain Ω, where ΔN∞ is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory.