The boundary value problem for Yang–Mills–Higgs fields

  • Wanjun Ai
  • Chong Song
  • Miaomiao ZhuEmail author


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 \(\alpha \rightarrow 1\). For \(\alpha >1\), some regularity results for \(\alpha \)-YMH field are shown. This is achieved by showing a regularity theorem for more general coupled systems, which extends the classical results of Ladyzhenskaya–Ural’ceva and Morrey.


Yang–Mills–Higgs Free boundary Neumann boundary Blow-up Regularity 

Mathematics Subject Classification

58E15 35J50 35R35 



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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingPeople’s Republic of China
  2. 2.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  3. 3.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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