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

Chang Shou Lin; Augusto C. Ponce; Yisong Yang

doi:10.1016/j.jfa.2007.03.010

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

Chang Shou Lin, Augusto C. Ponce, Yisong Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	289-350
Number of pages	62
Journal	Journal of Functional Analysis
Volume	247
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2007.03.010
State	Published - Jun 15 2007

Keywords

Elliptic equations
Gauge fields
Self-dual vortices
Topological solutions

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2007.03.010

Cite this

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title = "A system of elliptic equations arising in Chern-Simons field theory",

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.",

keywords = "Elliptic equations, Gauge fields, Self-dual vortices, Topological solutions",

author = "Lin, {Chang Shou} and Ponce, {Augusto C.} and Yisong Yang",

note = "Funding Information: The second author (A.C.P.) thanks H. Brezis and M. Montenegro for interesting discussions. The research of the third author (Y.Y.) was supported in part by the National Science Foundation under grant DMS-0406446 and by an Othmer Senior Faculty Fellowship.",

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T1 - A system of elliptic equations arising in Chern-Simons field theory

AU - Lin, Chang Shou

AU - Ponce, Augusto C.

AU - Yang, Yisong

N1 - Funding Information: The second author (A.C.P.) thanks H. Brezis and M. Montenegro for interesting discussions. The research of the third author (Y.Y.) was supported in part by the National Science Foundation under grant DMS-0406446 and by an Othmer Senior Faculty Fellowship.

PY - 2007/6/15

Y1 - 2007/6/15

N2 - 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.

AB - 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.

KW - Elliptic equations

KW - Gauge fields

KW - Self-dual vortices

KW - Topological solutions

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DO - 10.1016/j.jfa.2007.03.010

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EP - 350

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

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

Abstract

Keywords

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