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.