Phase separation of n dimensional infinity Harmonic mappings

TL;DR

This paper extends the analysis of phase separation phenomena in infinity Harmonic mappings from 2D to higher dimensions, exploring how solutions behave differently across phases in n-dimensional spaces.

Contribution

It generalizes Katzourakis's 2D results on phase separation in infinity Harmonic mappings to n-dimensional cases, advancing understanding of their solution structures.

Findings

Extended phase separation analysis to higher dimensions

Identified qualitative differences in solution behavior across phases

Provided theoretical framework for n-dimensional infinity Harmonic mappings

Abstract

Among other interesting results, in a recent paper, Katzourakis analysed the phenomenon of separation of the solutions to the infinity Laplace system to phases with qualitatively different behavior in the case of the 2 dimensional infinity Harmonic mappings. The solutions of the infinity Laplace system are called the infinity Harmonic mappings. In this paper we discuss an extension of Katzourakis result mentioned above to higher dimensions by studying the phase separation of n dimensional infinity Harmonic mappings.