Explicit $\mathrm{\infty }$-harmonic functions in high dimensions

The aim of this work is to derive new explicit solutions to the $\mathrm{\infty }$-Laplace equation, the fundamental PDE arising in Calculus of Variations in the space $L^{\mathrm{\infty }}$. 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.