On $\infty$-Ground States in the Plane

Abstract

We study $\infty$-Ground states in convex domains in the plane. In a polygon, the points where an $\infty$-Ground state does not satisfy the $\infty$-Laplace Equation are characterized: they are restricted to lie on specific curves, which are acting as attracting (fictitious) streamlines. The gradient is continuous outside these curves and no streamlines can meet there.

Two corollaries added