1. Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions.
- Author
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Bartolucci, Daniele, Gui, Changfeng, Hu, Yeyao, Jevnikar, Aleks, and Yang, Wen
- Subjects
LYAPUNOV-Schmidt equation ,BLOWING up (Algebraic geometry) ,TORUS ,EINSTEIN field equations ,EQUATIONS - Abstract
We are concerned with the blow-up analysis of mean field equations. It has been proven in [6] that solutions blowing-up at the same non-degenerate blow-up set are unique. On the other hand, the authors in [18] show that solutions with a degenerate blow-up set are in general non-unique. In this paper we first prove that evenly symmetric solutions on an arbitrary flat torus with a degenerate two-point blow-up set are unique. In the second part of the paper we complete the analysis by proving the existence of such blow-up solutions using a Lyapunov-Schmidt reduction method. Moreover, we deduce that all evenly symmetric blow-up solutions come from one-point blow-up solutions of the mean field equation on a "half" torus. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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