Explicit $\infty$-harmonic functions in high dimensions

Abstract

The aim of this work is to derive new explicit solutions to the $\infty$-Laplace equation, the fundamental PDE arising in Calculus of Variations in the space $L^{\infty }$. These solutions obey certain symmetry conditions and are derived in arbitrary dimensions, containing as particular sub-cases the already known classes two-dimensional infinity-harmonic functions.

14 pages, 28 figures