Explicit $$\infty$$ ∞ -harmonic functions in high dimensions

Abstract

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