Blow-up analysis for a cosmic strings equation

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• 作者：Gabriella Tarantello¹ ; ^{tarantel@mat.uniroma2.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Liouville-type equations ; Blow-up analysis ; Conical singularities
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：272
• 期：1
• 页码：255-338
• 全文大小：1090 K

文摘

In this paper we develop a blow-up analysis for solutions of an elliptic PDE of Liouville type over the plane. Such solutions describe the behavior of cosmic strings (parallel in a given direction) for a W-boson model coupled with Einstein's equation. We show how the blow-up behavior of the solutions is characterized, according to the physical parameters involved, by new and surprising phenomena. For example in some cases, after a suitable scaling, the blow-up profile of the solution is described in terms of an equations that bares a geometrical meaning in the context of the “uniformization” of the Riemann sphere with conical singularities.