A Convergent Semi-Lagrangian Scheme for the Game $$\infty $$ ∞ -Laplacian

Elisabetta Carlini () and Silvia Tozza ()
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Elisabetta Carlini: Sapienza University of Rome
Silvia Tozza: Alma Mater Studiorum University of Bologna

Dynamic Games and Applications, 2025, vol. 15, issue 2, No 4, 406-416

Abstract: Abstract We propose a new semi-Lagrangian scheme for the game $$\infty $$ ∞ -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.

Keywords: Game $$\infty $$ ∞ -Laplacian; Semi-Lagrangian scheme; Convergence analysis; Viscosity solutions; 65N06; 35J25; 35D40; 65N12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-024-00596-1

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