Elliptic Yang–Mills equation

We discuss some recent progress on the regularity theory of the elliptic Yang–Mills equation. We start with some basic properties of the elliptic Yang–Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang–Mills connections and compactness theorems on Yang–Mills connections with bounded L(2) norm of curvature. We also discuss in some detail self-dual solutions of the Yang–Mills equation and describe a compactification of their moduli space.