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.

引用

页数：11

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