Non-existence of solutions for a mean field equation on flat tori at critical parameter 16π

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin

研究成果: 雜誌貢獻文章

2 引文 斯高帕斯(Scopus)

摘要

It is known from [17] that the solvability of the mean field equation ∆u + eu = 8nπδ0 with n ∈ N 1 on a flat torus Eτ essentially depends on the geometry of Eτ. A conjecture is the non-existence of solutions for this equation if Eτ is a rectangular torus, which was proved for n = 1 in [17]. For any n ∈ N2, 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
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

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