Variational aspects of the Seiberg-Witten functional

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection A on a line bundleL and a section of another bundleW⁺ constructed fromL and a spinor bundle on a given four-dimensional Riemannian manifold. We show the regularity of weak solutions and the Palais-Smale condition for this functional.