A game theoretical approach for a nonlinear system driven by elliptic operators

Alfredo Miranda () and Julio D. Rossi ()
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Alfredo Miranda: Universidad de Buenos Aires
Julio D. Rossi: Universidad de Buenos Aires

Partial Differential Equations and Applications, 2020, vol. 1, issue 4, 1-41

Abstract: Abstract In this paper we find viscosity solutions to an elliptic system governed by two different operators (the Laplacian and the infinity Laplacian) using a probabilistic approach. We analyze a game that combines the tug-of-war with random walks in two different boards. We show that these value functions converge uniformly to a viscosity solution of the elliptic system as the step size goes to zero. In addition, we show uniqueness for the elliptic system using pure PDE techniques.

Keywords: 35J94; 35J47; 35J60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00014-2

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