Weakly coupled systems of the infinity Laplace equations

Mitake, H.; Tran, H.

doi:10.1090/tran6694

Weakly coupled systems of the infinity Laplace equations
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by H. Mitake and H. V. Tran PDF

Trans. Amer. Math. Soc. 369 (2017), 1773-1795 Request permission

Abstract:

We derive the weakly coupled systems of the infinity Laplace equations via a tug-of-war game introduced by Peres, Schramm, Sheffield, and Wilson (2009). We establish existence, uniqueness results of the solutions, and introduce a new notion of “generalized cones” for systems. By using “generalized cones” we analyze blow-up limits of solutions.

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