The boundary value problem for Yang--Mills--Higgs fields

Abstract

We show the existence of Yang--Mills--Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the convergence and blow-up behavior of a sequence of Sacks-Uhlenbeck type $\alpha$-YMH fields as $\alpha \to 1$. For $\alpha >1$, each $\alpha$-YMH field is shown to be smooth up to the boundary under some gauge transformation. This is achieved by showing a regularity theorem for more general coupled systems, which extends the classical results of Ladyzhenskaya-Ural'ceva and Morrey.

29 pages, no figures, all comments are welcome!

Cited by in corpus (2)

• Geometric analysis of the Yang-Mills-Higgs-Dirac model
• Trace theory for gauge-covariant Sobolev spaces