Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions

Tomohiko Sato; Takashi Suzuki

doi:10.4171/cmh/94

JournalscmhVol. 82, No. 2pp. 353–369

Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions

Tomohiko Sato
Osaka University, Japan
Takashi Suzuki
Osaka University, Japan

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Abstract

In this paper we study the asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem

- Δ v = λ V (x) e^{v} in Ω, v = 0 on \partial Ω,

where $Ω \subset R^{2}$ is a smooth bounded domain, $V (x)$ is a positive-valued $C^{1} (\overset{ˉ}{Ω})$ function, and $λ > 0$ is a constant.

Cite this article

Tomohiko Sato, Takashi Suzuki, Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions. Comment. Math. Helv. 82 (2007), no. 2, pp. 353–369

DOI 10.4171/CMH/94