On a System of Nonlinear Elliptic Equations Arising in Theoretical Physics

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Abstract

In this paper we study a system of nonlinear elliptic equations, known as the "vortex equations" in 2 dimensions, arising from the field-theoretical descriptions of several models in physics. When the underlying space is a closed surface, we prove the existence and uniqueness of a solution under a necessary and sufficient condition. When the space is R2, we establish the existence, uniqueness and sharp decay estimates for a solution.

Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalJournal of Functional Analysis
Volume170
Issue number1
DOIs
StatePublished - Jan 10 2000

ASJC Scopus subject areas

  • Analysis

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