The infinity-Laplacian in smooth convex domains and in a square

Abstract

We extend some theorems for the infinity-ground state and for the infinity-potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture.

Keywords

• the infinity-laplace operator
• nonlinear eigenvalue problem
• convex plane domains
• gradient flow
• alexandroff's moving plane