Weakly coupled systems of the infinity Laplace equations

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.

24 pages

References in corpus (1)

• An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions