Classification of stationary solutions of the $(4 + 1)$-dimensional radial Yang-Mills equation

TL;DR

This paper classifies all bounded classical solutions of a specific high-dimensional Yang-Mills related PDE, establishing symmetry properties and providing a complete solution characterization.

Contribution

It provides a comprehensive classification of solutions to a 4+1 dimensional radial Yang-Mills equation, including symmetry results for non-symmetric solutions.

Findings

Radially symmetric solutions are fully classified.

Bounded classical solutions are shown to be radially symmetric.

Complete solution classification achieved for the equation.

Abstract

We classify the solutions of the planar weighted Allen-Cahn equation arising from the critical equivariant $SO(4)$ Yang-Mills problem. We first give a complete classification for radially symmetric solutions, and then without symmetry assumptions, we show bounded classical solutions are radially symmetric and also classify them.