### 摘要

It is known from [17] that the solvability of the mean field equation ∆u + e^{u} = 8nπδ_{0} with n ∈ N_{≥} _{1} on a flat torus E_{τ} essentially depends on the geometry of E_{τ}. A conjecture is the non-existence of solutions for this equation if E_{τ} is a rectangular torus, which was proved for n = 1 in [17]. For any n ∈ N_{≥}2, this conjecture seems challenging from the viewpoint of PDE theory. In this paper, we prove this conjecture for n = 2 (i.e. at critical parameter 16π).

原文 | 英語 |
---|---|

頁（從 - 到） | 1737-1755 |

頁數 | 19 |

期刊 | Communications in Analysis and Geometry |

卷 | 27 |

發行號 | 8 |

DOIs | |

出版狀態 | 已發佈 - 2019 一月 1 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty

## 指紋 深入研究「Non-existence of solutions for a mean field equation on flat tori at critical parameter 16π」主題。共同形成了獨特的指紋。

## 引用此

Chen, Z., Kuo, T. J., & Lin, C. S. (2019). Non-existence of solutions for a mean field equation on flat tori at critical parameter 16π.

*Communications in Analysis and Geometry*,*27*(8), 1737-1755. https://doi.org/10.4310/cag.2019.v27.n8.a3