Solutions of Aronsson equation near isolated points

TL;DR

This paper investigates the behavior of non-negative solutions to the Aronsson equation near isolated singularities, showing they are either removable or asymptotically conical, extending previous results on infinity harmonic functions.

Contribution

It generalizes the asymptotic behavior theory for infinity harmonic functions to solutions of the Aronsson equation near isolated points.

Findings

Isolated singularities are either removable or asymptotically conical.

Extends the theory of asymptotic behavior for infinity harmonic functions.

Provides a classification of solution behavior near singularities.

Abstract

We show that for non-negative solution of the Aronsson equation an isolated singularity is either removable, or the solution behaves asymptotically like a general cone. This generalizes the asymptotic behavior theory for infinity harmonic functions by Savin, Wang and Yu.