Existence of solutions to the self-dual equations in the Maxwell gauged sigma model
type: Item
instance of: scholarly article
title: Existence of solutions to the self-dual equations in the Maxwell gauged sigma model
zbMATH Open document ID: 1229.35222
author: Jongmin Han
author: Hyungjin Huh
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-21T00:00:00Z
review text: The authors consider a self-dual Maxwell gauged \(O(3)\) sigma model. The existence of solutions for this model is proved by using the super and subsolution method. They obtain a subsolution by solving a Laplace equation on a weighted Sobolev space. The supersolutions are explicit constructed. Taking into account different values of a parameter which represents the decay rates of solutions at infinity, the subsolutions are given in different ways. So, if this parameter has noncritical values, the subsolutions are obtained via Laplace equation in Sobolev space, while if the above mentioned parameter is the critical number, the subsolutions are obtained via induction and shooting arguments.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q61
Mathematics Subject Classification ID: 70S15
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5960910
zbMATH Keywords: Maxwell gauged O(3) sigma model
zbMATH Keywords: super and subsolution method
zbMATH Keywords: self-dual equations
zbMATH Keywords: shooting arguments
reviewed by: Marin I. Marin
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.07.046
OpenAlex ID: W2004167986
cites work: Cauchy problems of the gauged sigma model
cites work: On the equation \(\Delta u+Ke^{2u}=f\) and prescribed negative curvature in \({\mathbb{R}}^ 2\)
cites work: Symmetry results for semilinear elliptic equations in \(\mathbb{R}^2\).
cites work: Q3961209
cites work: A necessary and sufficient condition for the existence of multisolitons in a self-dual gauged sigma model
DOI: 10.1016/J.JMAA.2011.07.046
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description: scientific article; zbMATH DE number 5960910