A Convergent Semi-Lagrangian Scheme for the Game ∞-Laplacian

被引：0
|
作者：
Carlini, Elisabetta [1 ]
Tozza, Silvia [2 ]
机构：
[1] Sapienza Univ Rome, Dept Math, Ple Aldo Moro 5, I-00185 Rome, RM, Italy
[2] Alma Mater Studiorum Univ Bologna, Dept Math, Pzza Porta S Donato 5, I-40126 Bologna, BO, Italy
来源：
DYNAMIC GAMES AND APPLICATIONS | 2024年
关键词：
Game infinity-Laplacian; Semi-Lagrangian scheme; Convergence analysis; Viscosity solutions; TUG-OF-WAR; VISCOSITY SOLUTIONS; EQUATIONS;
D O I：
10.1007/s13235-024-00596-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We propose a new semi-Lagrangian scheme for the game infinity-Laplacian. We demonstrate the convergence of the scheme to the viscosity solution of the given problem, showing its consistency, monotonicity, and stability. The proof of this result is established following the Barles-Souganidis analysis. This analysis assumes convergence at the boundary in a strong sense and is applied to our proposed scheme, augmented with an artificial viscosity term.
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页数：11
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