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Commentarii Mathematici Helvetici


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Volume 82, Issue 2, 2007, pp. 353–369
DOI: 10.4171/CMH/94

Published online: 2007-06-30

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

Tomohiko Sato[1] and Takashi Suzuki[2]

(1) Osaka University, Japan
(2) Osaka University, Japan

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

− Δv = λ V (x )ev in Ω,   v = 0 on ∂ Ω,
where Ω ⊂ ℝ2 is a smooth bounded domain, V (x ) is a positive-valued C1(Ω) function, and λ  > 0 is a constant.

Keywords: Liouville equation, blow-up analysis, Green's function

Sato Tomohiko, Suzuki Takashi: Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions. Comment. Math. Helv. 82 (2007), 353-369. doi: 10.4171/CMH/94