A semilinear partial differential equation induced by Hermitian Yang-Mills metrics

Abstract

This paper will discuss a class of semilinear partial differential equations induced by studying the limiting behaviour of Hermitian Yang-Mills metrics. We will study the radial symmetry of the $C^2$ global solution of this equation in ${\mathbb{R}}^2$ and the existence of $C^{2,\alpha }$ solution of the Dirichlet boundary value problem in any bounded domain.

6 pages