A system of elliptic equations arising in Chern-Simons field theory

Chang Shou Lin, Augusto C. Ponce, Yisong Yang

Research output: Contribution to journalArticlepeer-review


We prove the existence of topological vortices in a relativistic self-dual Abelian Chern-Simons theory with two Higgs particles and two gauge fields through a study of a coupled system of two nonlinear elliptic equations over R2. We present two approaches to prove existence of solutions on bounded domains: via minimization of an indefinite functional and via a fixed point argument. We then show that we may pass to the full R2 limit from the bounded-domain solutions to obtain a topological solution in R2.

Original languageEnglish (US)
Pages (from-to)289-350
Number of pages62
JournalJournal of Functional Analysis
Issue number2
StatePublished - Jun 15 2007


  • Elliptic equations
  • Gauge fields
  • Self-dual vortices
  • Topological solutions

ASJC Scopus subject areas

  • Analysis


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