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

Chang Shou Lin, Augusto C. Ponce, Yisong Yang

Research output: Contribution to journalArticle

Abstract

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
Volume247
Issue number2
DOIs
StatePublished - Jun 15 2007

Fingerprint

Chern-Simons Theories
Elliptic Equations
Field Theory
Bounded Domain
Nonlinear Elliptic Equations
Gauge Field
Higgs
Coupled System
Existence of Solutions
Vortex
Fixed point

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

A system of elliptic equations arising in Chern-Simons field theory. / Lin, Chang Shou; Ponce, Augusto C.; Yang, Yisong.

In: Journal of Functional Analysis, Vol. 247, No. 2, 15.06.2007, p. 289-350.

Research output: Contribution to journalArticle

Lin, Chang Shou ; Ponce, Augusto C. ; Yang, Yisong. / A system of elliptic equations arising in Chern-Simons field theory. In: Journal of Functional Analysis. 2007 ; Vol. 247, No. 2. pp. 289-350.
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