arXiv:2003.08969 Abstract | arXiv Analytics

arXiv:2003.08969 [math.AP]Abstract References Reviews Resources

A game theoretical approach for an elliptic system with two different operators (the Laplacian and the infinity Laplacian)

Published 2020-03-19Version 1

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 boars. 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.

Categories: math.AP, math.PR

Keywords: elliptic system, game theoretical approach, infinity laplacian, viscosity solution, pure pde techniques

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